%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG012-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:57:46 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.51s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG012-1 : TPTP v9.0.0. Released v2.7.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 10:41:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.51 % SZS status Unsatisfiable
% 0.18/0.51 % SZS output start Proof
% 0.18/0.51 tff(c_type, type, (
% 0.18/0.51 c: $i > $o)).
% 0.18/0.51 tff(f_type, type, (
% 0.18/0.51 f: ( $i * $i ) > $i)).
% 0.18/0.51 tff(a3_type, type, (
% 0.18/0.51 a3: $i)).
% 0.18/0.51 tff(d1_type, type, (
% 0.18/0.51 d1: $i > $o)).
% 0.18/0.51 tff(d2_type, type, (
% 0.18/0.51 d2: $i > $o)).
% 0.18/0.51 tff(a1_type, type, (
% 0.18/0.51 a1: $i)).
% 0.18/0.51 tff(1,plain,
% 0.18/0.51 (^[Z: $i, Y: $i, X: $i] : refl((f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> (f(X, f(Y, Z)) = f(f(X, Y), Z)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(2,plain,
% 0.18/0.51 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.51 tff(3,plain,
% 0.18/0.51 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(4,axiom,(![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f_is_associative')).
% 0.18/0.51 tff(5,plain,
% 0.18/0.51 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.51 tff(6,plain,(
% 0.18/0.51 ![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.51 inference(skolemize,[status(sab)],[5])).
% 0.18/0.51 tff(7,plain,
% 0.18/0.51 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.51 tff(8,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a3, a3), f(a3, a3)) = f(f(f(a3, a3), a3), a3))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(9,plain,
% 0.18/0.51 (f(f(a3, a3), f(a3, a3)) = f(f(f(a3, a3), a3), a3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.51 tff(10,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), a3) = f(f(a3, a3), f(a3, a3))),
% 0.18/0.51 inference(symmetry,[status(thm)],[9])).
% 0.18/0.51 tff(11,plain,
% 0.18/0.51 (d2(f(f(f(a3, a3), a3), a3)) <=> d2(f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.51 tff(12,plain,
% 0.18/0.51 (d2(f(f(a3, a3), f(a3, a3))) <=> d2(f(f(f(a3, a3), a3), a3))),
% 0.18/0.51 inference(symmetry,[status(thm)],[11])).
% 0.18/0.51 tff(13,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(14,plain,
% 0.18/0.51 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[13, 7])).
% 0.18/0.51 tff(15,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(16,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[15, 7])).
% 0.18/0.51 tff(17,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))) = f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[9])).
% 0.18/0.51 tff(18,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)),
% 0.18/0.51 inference(transitivity,[status(thm)],[17, 16])).
% 0.18/0.51 tff(19,plain,
% 0.18/0.51 (f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[18])).
% 0.18/0.51 tff(20,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))) = f(f(f(f(a3, a3), a3), f(a3, a3)), f(a3, a3)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(21,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))) = f(f(f(f(a3, a3), a3), f(a3, a3)), f(a3, a3))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[20, 7])).
% 0.18/0.51 tff(22,plain,
% 0.18/0.51 (f(f(f(f(a3, a3), a3), f(a3, a3)), f(a3, a3)) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(symmetry,[status(thm)],[21])).
% 0.18/0.51 tff(23,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a3, a3), f(a3, f(a3, a3))) = f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(24,plain,
% 0.18/0.51 (f(f(a3, a3), f(a3, f(a3, a3))) = f(f(f(a3, a3), a3), f(a3, a3))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[23, 7])).
% 0.18/0.51 tff(25,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a3, f(a3, a3)) = f(f(a3, a3), a3))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(26,plain,
% 0.18/0.51 (f(a3, f(a3, a3)) = f(f(a3, a3), a3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[25, 7])).
% 0.18/0.51 tff(27,plain,
% 0.18/0.51 (f(f(a3, a3), f(a3, f(a3, a3))) = f(f(a3, a3), f(f(a3, a3), a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[26])).
% 0.18/0.51 tff(28,plain,
% 0.18/0.51 (f(f(a3, a3), f(f(a3, a3), a3)) = f(f(a3, a3), f(a3, f(a3, a3)))),
% 0.18/0.51 inference(symmetry,[status(thm)],[27])).
% 0.18/0.51 tff(29,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a3, a3), f(f(a3, a3), a3)) = f(f(f(a3, a3), f(a3, a3)), a3))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(30,plain,
% 0.18/0.51 (f(f(a3, a3), f(f(a3, a3), a3)) = f(f(f(a3, a3), f(a3, a3)), a3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[29, 7])).
% 0.18/0.51 tff(31,plain,
% 0.18/0.51 (f(f(f(a3, a3), f(a3, a3)), a3) = f(f(a3, a3), f(f(a3, a3), a3))),
% 0.18/0.51 inference(symmetry,[status(thm)],[30])).
% 0.18/0.51 tff(32,plain,
% 0.18/0.51 (f(f(a3, f(a3, a3)), a3) = f(f(f(a3, a3), a3), a3)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[26])).
% 0.18/0.51 tff(33,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), a3) = f(f(a3, f(a3, a3)), a3)),
% 0.18/0.51 inference(symmetry,[status(thm)],[32])).
% 0.18/0.51 tff(34,plain,
% 0.18/0.51 (f(f(a3, a3), f(a3, a3)) = f(f(a3, f(a3, a3)), a3)),
% 0.18/0.51 inference(transitivity,[status(thm)],[9, 33])).
% 0.18/0.51 tff(35,plain,
% 0.18/0.51 (f(f(f(a3, a3), f(a3, a3)), a3) = f(f(f(a3, f(a3, a3)), a3), a3)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[34])).
% 0.18/0.51 tff(36,plain,
% 0.18/0.51 (f(f(f(a3, f(a3, a3)), a3), a3) = f(f(f(a3, a3), f(a3, a3)), a3)),
% 0.18/0.51 inference(symmetry,[status(thm)],[35])).
% 0.18/0.51 tff(37,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a3, f(a3, a3)), f(a3, a3)) = f(f(f(a3, f(a3, a3)), a3), a3))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(38,plain,
% 0.18/0.51 (f(f(a3, f(a3, a3)), f(a3, a3)) = f(f(f(a3, f(a3, a3)), a3), a3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[37, 7])).
% 0.18/0.51 tff(39,plain,
% 0.18/0.51 (f(f(a3, f(a3, a3)), f(a3, a3)) = f(f(f(a3, a3), a3), f(a3, a3))),
% 0.18/0.51 inference(transitivity,[status(thm)],[38, 36, 31, 28, 24])).
% 0.18/0.51 tff(40,plain,
% 0.18/0.51 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)) = f(f(f(f(a3, a3), a3), f(a3, a3)), f(a3, a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[39])).
% 0.18/0.51 tff(41,plain,
% 0.18/0.51 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[40, 22])).
% 0.18/0.51 tff(42,plain,
% 0.18/0.51 (f(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.51 tff(43,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), f(f(a3, a3), a3))) = f(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(44,plain,
% 0.18/0.51 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), f(f(a3, a3), a3))) = f(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[43, 7])).
% 0.18/0.51 tff(45,plain,
% 0.18/0.51 (f(f(a3, f(a3, a3)), f(a3, a3)) = f(f(a3, a3), f(f(a3, a3), a3))),
% 0.18/0.51 inference(transitivity,[status(thm)],[38, 36, 31])).
% 0.18/0.51 tff(46,plain,
% 0.18/0.51 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), f(f(a3, a3), a3)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[45])).
% 0.18/0.51 tff(47,plain,
% 0.18/0.51 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)),
% 0.18/0.51 inference(transitivity,[status(thm)],[46, 44, 42, 19, 14])).
% 0.18/0.51 tff(48,plain,
% 0.18/0.51 (c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))) <=> c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.51 tff(49,plain,
% 0.18/0.51 (c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) <=> c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.18/0.51 inference(symmetry,[status(thm)],[48])).
% 0.18/0.51 tff(50,plain,
% 0.18/0.51 ((~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) <=> (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.51 tff(51,plain,
% 0.18/0.51 (f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))),
% 0.18/0.51 inference(symmetry,[status(thm)],[14])).
% 0.18/0.51 tff(52,plain,
% 0.18/0.51 (d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) <=> d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.51 tff(53,plain,
% 0.18/0.51 (d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))) <=> d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.18/0.51 inference(symmetry,[status(thm)],[52])).
% 0.18/0.51 tff(54,plain,
% 0.18/0.51 (f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(symmetry,[status(thm)],[17])).
% 0.18/0.51 tff(55,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a3, a3), f(a3, f(f(f(a3, a3), a3), a3))) = f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(56,plain,
% 0.18/0.51 (f(f(a3, a3), f(a3, f(f(f(a3, a3), a3), a3))) = f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[55, 7])).
% 0.18/0.51 tff(57,plain,
% 0.18/0.51 (f(a3, f(f(f(a3, a3), a3), a3)) = f(a3, f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.51 tff(58,plain,
% 0.18/0.51 (f(a3, f(f(a3, a3), f(a3, a3))) = f(a3, f(f(f(a3, a3), a3), a3))),
% 0.18/0.51 inference(symmetry,[status(thm)],[57])).
% 0.18/0.51 tff(59,assumption,(~(f(a3, f(f(a3, a3), f(a3, a3))) = f(f(a3, f(a3, a3)), f(a3, a3)))), introduced(assumption)).
% 0.18/0.51 tff(60,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a3, f(f(a3, a3), f(a3, a3))) = f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(61,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[60, 7, 59])).
% 0.18/0.51 tff(62,plain,(f(a3, f(f(a3, a3), f(a3, a3))) = f(f(a3, f(a3, a3)), f(a3, a3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(63,plain,
% 0.18/0.51 (f(f(a3, f(a3, a3)), f(a3, a3)) = f(a3, f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(symmetry,[status(thm)],[62])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 (f(f(a3, f(a3, a3)), f(a3, a3)) = f(a3, f(f(f(a3, a3), a3), a3))),
% 0.18/0.51 inference(transitivity,[status(thm)],[63, 58])).
% 0.18/0.51 tff(65,plain,
% 0.18/0.51 (f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(a3, a3), f(a3, f(f(f(a3, a3), a3), a3)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[64])).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 (f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[65, 56, 54])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (f(f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3))), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))) = f(f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3))), f(f(a3, a3), a3)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 (f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))) = f(f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3))), f(f(a3, a3), a3))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[68, 7])).
% 0.18/0.51 tff(70,plain,
% 0.18/0.51 (f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))),
% 0.18/0.51 inference(transitivity,[status(thm)],[69, 67, 19])).
% 0.18/0.51 tff(71,plain,
% 0.18/0.51 (d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) <=> d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.51 tff(72,plain,
% 0.18/0.51 (d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) <=> d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.36/0.52 inference(transitivity,[status(thm)],[71, 53])).
% 0.36/0.52 tff(73,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(74,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[73, 7])).
% 0.36/0.52 tff(75,plain,
% 0.36/0.52 (f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3) = f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))),
% 0.36/0.52 inference(symmetry,[status(thm)],[74])).
% 0.36/0.52 tff(76,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, a3), a3), f(a3, f(f(a3, a3), a3))) = f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(77,plain,
% 0.36/0.52 (f(f(f(a3, a3), a3), f(a3, f(f(a3, a3), a3))) = f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[76, 7])).
% 0.36/0.52 tff(78,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a3, f(a3, f(a3, a3))) = f(f(a3, a3), f(a3, a3)))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(79,plain,
% 0.36/0.52 (f(a3, f(a3, f(a3, a3))) = f(f(a3, a3), f(a3, a3))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[78, 7])).
% 0.36/0.52 tff(80,plain,
% 0.36/0.52 (f(f(a3, a3), a3) = f(a3, f(a3, a3))),
% 0.36/0.52 inference(symmetry,[status(thm)],[26])).
% 0.36/0.52 tff(81,plain,
% 0.36/0.52 (f(a3, f(f(a3, a3), a3)) = f(a3, f(a3, f(a3, a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[80])).
% 0.36/0.52 tff(82,plain,
% 0.36/0.52 (f(a3, f(f(a3, a3), a3)) = f(f(a3, a3), f(a3, a3))),
% 0.36/0.52 inference(transitivity,[status(thm)],[81, 79])).
% 0.36/0.52 tff(83,plain,
% 0.36/0.52 (f(f(f(a3, a3), a3), f(a3, f(f(a3, a3), a3))) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[82])).
% 0.36/0.52 tff(84,plain,
% 0.36/0.52 (f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))) = f(f(f(a3, a3), a3), f(a3, f(f(a3, a3), a3)))),
% 0.36/0.52 inference(symmetry,[status(thm)],[83])).
% 0.36/0.52 tff(85,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3) = f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3))),
% 0.36/0.52 inference(symmetry,[status(thm)],[16])).
% 0.36/0.52 tff(86,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3) = f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3))),
% 0.36/0.52 inference(transitivity,[status(thm)],[85, 54, 84, 77])).
% 0.36/0.52 tff(87,plain,
% 0.36/0.52 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), a3) = f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3)),
% 0.36/0.52 inference(monotonicity,[status(thm)],[86])).
% 0.36/0.52 tff(88,plain,
% 0.36/0.52 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)),
% 0.36/0.52 inference(transitivity,[status(thm)],[40, 22, 17, 16])).
% 0.36/0.52 tff(89,plain,
% 0.36/0.52 (f(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)), a3) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), a3)),
% 0.36/0.52 inference(monotonicity,[status(thm)],[88])).
% 0.36/0.52 tff(90,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)) = f(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)), a3))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(91,plain,
% 0.36/0.52 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)) = f(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)), a3)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[90, 7])).
% 0.36/0.52 tff(92,plain,
% 0.36/0.52 (f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))),
% 0.36/0.52 inference(transitivity,[status(thm)],[91, 89, 87, 75])).
% 0.36/0.52 tff(93,plain,
% 0.36/0.52 (c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))) <=> c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[92])).
% 0.36/0.52 tff(94,plain,
% 0.36/0.52 (c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))) <=> c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))),
% 0.36/0.52 inference(symmetry,[status(thm)],[93])).
% 0.36/0.52 tff(95,plain,
% 0.36/0.52 (d1(f(f(f(a3, a3), a3), a3)) <=> d1(f(f(a3, a3), f(a3, a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[10])).
% 0.36/0.52 tff(96,plain,
% 0.36/0.52 (d1(f(f(a3, a3), f(a3, a3))) <=> d1(f(f(f(a3, a3), a3), a3))),
% 0.36/0.52 inference(symmetry,[status(thm)],[95])).
% 0.36/0.52 tff(97,assumption,(d1(f(f(a3, a3), f(a3, a3)))), introduced(assumption)).
% 0.36/0.52 tff(98,plain,
% 0.36/0.52 (d1(f(f(f(a3, a3), a3), a3))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.36/0.52 tff(99,plain,
% 0.36/0.52 (^[Y: $i, X: $i] : refl(((~d1(X)) | (~d1(Y)) | c(f(X, Y))) <=> ((~d1(X)) | (~d1(Y)) | c(f(X, Y))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(100,plain,
% 0.36/0.52 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y))) <=> ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[99])).
% 0.36/0.52 tff(101,plain,
% 0.36/0.52 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y))) <=> ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(102,plain,
% 0.36/0.52 (^[Y: $i, X: $i] : rewrite(((c(f(X, Y)) | (~d1(X))) | (~d1(Y))) <=> ((~d1(X)) | (~d1(Y)) | c(f(X, Y))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(103,plain,
% 0.36/0.52 (![Y: $i, X: $i] : ((c(f(X, Y)) | (~d1(X))) | (~d1(Y))) <=> ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[102])).
% 0.36/0.52 tff(104,axiom,(![Y: $i, X: $i] : ((c(f(X, Y)) | (~d1(X))) | (~d1(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture_2')).
% 0.36/0.52 tff(105,plain,
% 0.36/0.52 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.36/0.52 tff(106,plain,
% 0.36/0.52 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.36/0.52 tff(107,plain,(
% 0.36/0.52 ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(skolemize,[status(sab)],[106])).
% 0.36/0.52 tff(108,plain,
% 0.36/0.52 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.36/0.52 tff(109,plain,
% 0.36/0.52 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(110,plain,
% 0.36/0.52 (((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))) <=> ((~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(111,plain,
% 0.36/0.52 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[110])).
% 0.36/0.52 tff(112,plain,
% 0.36/0.52 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[111, 109])).
% 0.36/0.52 tff(113,plain,
% 0.36/0.52 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(114,plain,
% 0.36/0.52 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.36/0.52 tff(115,plain,
% 0.36/0.52 (c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[114, 108, 98])).
% 0.36/0.52 tff(116,plain,
% 0.36/0.52 (c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[115, 94])).
% 0.36/0.52 tff(117,plain,
% 0.36/0.52 (d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) <=> d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[70])).
% 0.36/0.52 tff(118,plain,
% 0.36/0.52 (d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))) <=> d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.36/0.52 inference(symmetry,[status(thm)],[117])).
% 0.36/0.52 tff(119,plain,
% 0.36/0.52 ((~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))) <=> (~d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[118])).
% 0.36/0.52 tff(120,plain,
% 0.36/0.52 (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))) <=> d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[19])).
% 0.36/0.52 tff(121,plain,
% 0.36/0.52 ((~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))) <=> (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[120])).
% 0.36/0.52 tff(122,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[17])).
% 0.36/0.52 tff(123,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3))) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.36/0.52 inference(symmetry,[status(thm)],[122])).
% 0.36/0.52 tff(124,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3))) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(125,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3))) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[124, 7])).
% 0.36/0.52 tff(126,plain,
% 0.36/0.52 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(symmetry,[status(thm)],[125])).
% 0.36/0.52 tff(127,plain,
% 0.36/0.52 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[126, 123])).
% 0.36/0.52 tff(128,plain,
% 0.36/0.52 (c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) <=> c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[127])).
% 0.36/0.52 tff(129,plain,
% 0.36/0.52 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) <=> c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(symmetry,[status(thm)],[128])).
% 0.36/0.52 tff(130,plain,
% 0.36/0.52 ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) <=> (~c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[129])).
% 0.36/0.52 tff(131,plain,
% 0.36/0.52 (c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3)) <=> c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[75])).
% 0.36/0.52 tff(132,plain,
% 0.36/0.52 (c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3))) <=> c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))),
% 0.36/0.52 inference(symmetry,[status(thm)],[131])).
% 0.36/0.52 tff(133,plain,
% 0.36/0.52 (c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[115, 132])).
% 0.36/0.52 tff(134,plain,
% 0.36/0.52 (f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)) = f(f(f(a3, a3), a3), f(a3, f(f(a3, a3), a3)))),
% 0.36/0.52 inference(symmetry,[status(thm)],[77])).
% 0.36/0.53 tff(135,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.36/0.53 inference(transitivity,[status(thm)],[134, 83])).
% 0.36/0.53 tff(136,plain,
% 0.36/0.53 (f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[135])).
% 0.36/0.53 tff(137,plain,
% 0.36/0.53 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), f(f(a3, a3), a3))) = f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), f(f(a3, a3), a3)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(138,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), f(f(a3, a3), a3))) = f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), f(f(a3, a3), a3))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[137, 7])).
% 0.36/0.53 tff(139,plain,
% 0.36/0.53 (f(f(f(a3, a3), a3), f(a3, f(a3, a3))) = f(f(f(a3, a3), a3), f(f(a3, a3), a3))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[26])).
% 0.36/0.53 tff(140,plain,
% 0.36/0.53 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, a3), a3), f(a3, f(a3, a3))) = f(f(f(f(a3, a3), a3), a3), f(a3, a3)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(141,plain,
% 0.36/0.53 (f(f(f(a3, a3), a3), f(a3, f(a3, a3))) = f(f(f(f(a3, a3), a3), a3), f(a3, a3))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[140, 7])).
% 0.36/0.53 tff(142,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), a3), f(a3, a3)) = f(f(f(a3, a3), a3), f(a3, f(a3, a3)))),
% 0.36/0.53 inference(symmetry,[status(thm)],[141])).
% 0.36/0.53 tff(143,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), a3), f(a3, a3)) = f(f(f(a3, a3), a3), f(f(a3, a3), a3))),
% 0.36/0.53 inference(transitivity,[status(thm)],[142, 139])).
% 0.36/0.53 tff(144,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), a3), f(f(f(f(a3, a3), a3), a3), f(a3, a3))) = f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[143])).
% 0.36/0.53 tff(145,plain,
% 0.36/0.53 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a3, a3), a3), a3), f(f(f(f(a3, a3), a3), a3), f(a3, a3))) = f(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)), f(a3, a3)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(146,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), a3), f(f(f(f(a3, a3), a3), a3), f(a3, a3))) = f(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)), f(a3, a3))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[145, 7])).
% 0.36/0.53 tff(147,plain,
% 0.36/0.53 (f(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)), f(a3, a3)) = f(f(f(f(a3, a3), a3), a3), f(f(f(f(a3, a3), a3), a3), f(a3, a3)))),
% 0.36/0.53 inference(symmetry,[status(thm)],[146])).
% 0.36/0.53 tff(148,plain,
% 0.36/0.53 (f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)) = f(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)), f(a3, a3))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[75])).
% 0.36/0.53 tff(149,plain,
% 0.36/0.53 (f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)),
% 0.36/0.53 inference(transitivity,[status(thm)],[148, 147, 144, 138, 136, 19, 14])).
% 0.36/0.53 tff(150,plain,
% 0.36/0.53 (d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) <=> d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[149])).
% 0.36/0.53 tff(151,plain,
% 0.36/0.53 (d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) <=> d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.36/0.53 inference(symmetry,[status(thm)],[150])).
% 0.36/0.53 tff(152,plain,
% 0.36/0.53 ((~d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) <=> (~d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[151])).
% 0.36/0.53 tff(153,plain,
% 0.36/0.53 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), f(a3, f(f(a3, a3), a3))) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(154,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), f(a3, f(f(a3, a3), a3))) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[153, 7])).
% 0.36/0.53 tff(155,plain,
% 0.36/0.53 (f(a3, f(a3, f(a3, a3))) = f(a3, f(f(a3, a3), a3))),
% 0.36/0.53 inference(symmetry,[status(thm)],[81])).
% 0.36/0.53 tff(156,plain,
% 0.36/0.53 (f(f(a3, a3), f(a3, a3)) = f(a3, f(a3, f(a3, a3)))),
% 0.36/0.53 inference(symmetry,[status(thm)],[79])).
% 0.36/0.53 tff(157,plain,
% 0.36/0.53 (f(f(f(a3, a3), a3), a3) = f(a3, f(f(a3, a3), a3))),
% 0.36/0.53 inference(transitivity,[status(thm)],[10, 156, 155])).
% 0.36/0.53 tff(158,plain,
% 0.36/0.53 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, a3), a3), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), f(a3, a3)), a3))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(159,plain,
% 0.36/0.53 (f(f(f(a3, a3), a3), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), f(a3, a3)), a3)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[158, 7])).
% 0.36/0.53 tff(160,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), f(a3, a3)), a3) = f(f(f(a3, a3), a3), f(f(a3, a3), a3))),
% 0.36/0.53 inference(symmetry,[status(thm)],[159])).
% 0.36/0.53 tff(161,plain,
% 0.36/0.53 (f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), f(a3, f(f(a3, a3), a3)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[160, 157])).
% 0.36/0.53 tff(162,plain,
% 0.36/0.53 (f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)),
% 0.36/0.53 inference(transitivity,[status(thm)],[161, 154, 14])).
% 0.36/0.53 tff(163,plain,
% 0.36/0.53 (c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))) <=> c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[162])).
% 0.36/0.53 tff(164,plain,
% 0.36/0.53 (d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3)) <=> d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[160])).
% 0.36/0.53 tff(165,plain,
% 0.36/0.53 (d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) <=> d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))),
% 0.36/0.53 inference(symmetry,[status(thm)],[164])).
% 0.36/0.53 tff(166,plain,
% 0.36/0.53 (f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3) = f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))),
% 0.36/0.53 inference(transitivity,[status(thm)],[85, 54])).
% 0.36/0.53 tff(167,plain,
% 0.36/0.53 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)) <=> c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[166])).
% 0.36/0.53 tff(168,plain,
% 0.36/0.53 (c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) <=> c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.36/0.53 inference(symmetry,[status(thm)],[167])).
% 0.36/0.53 tff(169,plain,
% 0.36/0.53 ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) <=> (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[168])).
% 0.36/0.53 tff(170,assumption,(~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))), introduced(assumption)).
% 0.36/0.53 tff(171,plain,
% 0.36/0.53 (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.36/0.53 tff(172,plain,
% 0.36/0.53 (^[Y: $i, X: $i] : refl(((~d2(X)) | c(f(X, Y)) | (~d2(Y))) <=> ((~d2(X)) | c(f(X, Y)) | (~d2(Y))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(173,plain,
% 0.36/0.53 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y))) <=> ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[172])).
% 0.36/0.53 tff(174,plain,
% 0.36/0.53 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y))) <=> ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(175,plain,
% 0.36/0.53 (^[Y: $i, X: $i] : rewrite(((c(f(X, Y)) | (~d2(X))) | (~d2(Y))) <=> ((~d2(X)) | c(f(X, Y)) | (~d2(Y))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(176,plain,
% 0.36/0.53 (![Y: $i, X: $i] : ((c(f(X, Y)) | (~d2(X))) | (~d2(Y))) <=> ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[175])).
% 0.36/0.53 tff(177,axiom,(![Y: $i, X: $i] : ((c(f(X, Y)) | (~d2(X))) | (~d2(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture_3')).
% 0.36/0.53 tff(178,plain,
% 0.36/0.53 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.36/0.53 tff(179,plain,
% 0.36/0.53 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.36/0.53 tff(180,plain,(
% 0.36/0.53 ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.37/0.53 inference(skolemize,[status(sab)],[179])).
% 0.37/0.53 tff(181,plain,
% 0.37/0.53 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.37/0.53 tff(182,plain,
% 0.37/0.53 (d2(a3) <=> d2(a3)),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(183,axiom,(d2(a3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','partition_d2_not_empty')).
% 0.37/0.53 tff(184,plain,
% 0.37/0.53 (d2(a3)),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.37/0.53 tff(185,plain,
% 0.37/0.53 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(186,plain,
% 0.37/0.53 (((~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)) | (~d2(a3))) <=> ((~d2(a3)) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(187,plain,
% 0.37/0.53 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[186])).
% 0.37/0.53 tff(188,plain,
% 0.37/0.53 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[187, 185])).
% 0.37/0.53 tff(189,plain,
% 0.37/0.53 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)) | (~d2(a3)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(190,plain,
% 0.37/0.53 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.37/0.53 tff(191,plain,
% 0.37/0.53 ((~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[190, 184, 181])).
% 0.37/0.53 tff(192,plain,
% 0.37/0.53 (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[191, 171])).
% 0.37/0.53 tff(193,plain,
% 0.37/0.53 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(194,plain,
% 0.37/0.53 (((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), f(a3, a3)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) <=> (c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(195,plain,
% 0.37/0.53 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), f(a3, a3)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3)))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[194])).
% 0.37/0.53 tff(196,plain,
% 0.37/0.53 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), f(a3, a3)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[195, 193])).
% 0.37/0.54 tff(197,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), f(a3, a3)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(198,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.37/0.54 tff(199,plain,
% 0.37/0.54 (c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), a3)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[198, 108])).
% 0.37/0.54 tff(200,plain,
% 0.37/0.54 (~d1(f(f(a3, a3), a3))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[199, 170, 97])).
% 0.37/0.54 tff(201,plain,
% 0.37/0.54 (^[X: $i] : refl(((~c(X)) | (~d1(X))) <=> ((~c(X)) | (~d1(X))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(202,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d1(X))) <=> ![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[201])).
% 0.37/0.54 tff(203,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d1(X))) <=> ![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(204,axiom,(![X: $i] : ((~c(X)) | (~d1(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','partitions_exclusive_c_d1')).
% 0.37/0.54 tff(205,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.37/0.54 tff(206,plain,(
% 0.37/0.54 ![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[205])).
% 0.37/0.54 tff(207,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.37/0.54 tff(208,plain,
% 0.37/0.54 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(209,plain,
% 0.37/0.54 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(210,plain,
% 0.37/0.54 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.37/0.54 tff(211,plain,
% 0.37/0.54 (~c(f(f(f(a3, a3), a3), a3))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[210, 207, 98])).
% 0.37/0.54 tff(212,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | (~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | (~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(213,plain,
% 0.37/0.54 (((~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)) | (~d2(a3))) <=> ((~d2(a3)) | (~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(214,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | (~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[213])).
% 0.37/0.54 tff(215,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | (~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(transitivity,[status(thm)],[214, 212])).
% 0.37/0.54 tff(216,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3)) | (~d2(a3)))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(217,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | (~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.37/0.54 tff(218,plain,
% 0.37/0.54 ((~d2(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), a3))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[217, 184, 181])).
% 0.37/0.54 tff(219,plain,
% 0.37/0.54 (~d2(f(f(a3, a3), a3))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[218, 211])).
% 0.37/0.54 tff(220,plain,
% 0.37/0.54 (^[X: $i] : refl((d2(X) | d1(X) | c(X)) <=> (d2(X) | d1(X) | c(X)))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(221,plain,
% 0.37/0.54 (![X: $i] : (d2(X) | d1(X) | c(X)) <=> ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[220])).
% 0.37/0.54 tff(222,plain,
% 0.37/0.54 (![X: $i] : (d2(X) | d1(X) | c(X)) <=> ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(223,plain,
% 0.37/0.54 (^[X: $i] : rewrite(((c(X) | d1(X)) | d2(X)) <=> (d2(X) | d1(X) | c(X)))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(224,plain,
% 0.37/0.54 (![X: $i] : ((c(X) | d1(X)) | d2(X)) <=> ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[223])).
% 0.37/0.54 tff(225,axiom,(![X: $i] : ((c(X) | d1(X)) | d2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','partitions_union')).
% 0.37/0.54 tff(226,plain,
% 0.37/0.54 (![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.37/0.54 tff(227,plain,
% 0.37/0.54 (![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.37/0.54 tff(228,plain,(
% 0.37/0.54 ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(skolemize,[status(sab)],[227])).
% 0.37/0.54 tff(229,plain,
% 0.37/0.54 (![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.37/0.54 tff(230,plain,
% 0.37/0.54 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3)))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(231,plain,
% 0.37/0.54 ((d2(f(f(a3, a3), a3)) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3))) <=> (d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(232,plain,
% 0.37/0.54 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a3, a3), a3)) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[231])).
% 0.37/0.54 tff(233,plain,
% 0.37/0.54 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a3, a3), a3)) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3)))),
% 0.37/0.54 inference(transitivity,[status(thm)],[232, 230])).
% 0.37/0.54 tff(234,plain,
% 0.37/0.54 ((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a3, a3), a3)) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(235,plain,
% 0.37/0.54 ((~![X: $i] : (d2(X) | d1(X) | c(X))) | d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.37/0.54 tff(236,plain,
% 0.37/0.54 (d1(f(f(a3, a3), a3)) | c(f(f(a3, a3), a3))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[235, 229, 219])).
% 0.37/0.54 tff(237,plain,
% 0.37/0.54 (c(f(f(a3, a3), a3))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[236, 200])).
% 0.37/0.54 tff(238,plain,
% 0.37/0.54 (^[Y: $i, X: $i] : refl(((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))) <=> ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(239,plain,
% 0.37/0.54 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))) <=> ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[238])).
% 0.37/0.54 tff(240,plain,
% 0.37/0.54 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))) <=> ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(241,plain,
% 0.37/0.54 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((d2(f(X, Y)) | d1(f(X, Y))) <=> (d1(f(X, Y)) | d2(f(X, Y)))), (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) <=> ((d1(f(X, Y)) | d2(f(X, Y))) | (~c(X))))), rewrite(((d1(f(X, Y)) | d2(f(X, Y))) | (~c(X))) <=> ((~c(X)) | d1(f(X, Y)) | d2(f(X, Y)))), (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) <=> ((~c(X)) | d1(f(X, Y)) | d2(f(X, Y))))), ((((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y))) <=> (((~c(X)) | d1(f(X, Y)) | d2(f(X, Y))) | (~c(Y))))), rewrite((((~c(X)) | d1(f(X, Y)) | d2(f(X, Y))) | (~c(Y))) <=> ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))), ((((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y))) <=> ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(242,plain,
% 0.37/0.54 (![Y: $i, X: $i] : (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y))) <=> ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[241])).
% 0.37/0.54 tff(243,axiom,(![Y: $i, X: $i] : (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture_1')).
% 0.37/0.54 tff(244,plain,
% 0.37/0.54 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.37/0.54 tff(245,plain,
% 0.37/0.54 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.37/0.54 tff(246,plain,(
% 0.37/0.54 ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[245])).
% 0.37/0.54 tff(247,plain,
% 0.37/0.54 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.37/0.54 tff(248,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(249,plain,
% 0.37/0.54 (((~c(f(f(a3, a3), a3))) | (~c(f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) <=> ((~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(250,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | (~c(f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[249])).
% 0.37/0.54 tff(251,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | (~c(f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[250, 248])).
% 0.37/0.54 tff(252,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | (~c(f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(253,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.37/0.54 tff(254,plain,
% 0.37/0.54 (d2(f(f(f(a3, a3), a3), f(f(a3, a3), a3))) | d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[253, 247, 237])).
% 0.37/0.54 tff(255,plain,
% 0.37/0.54 (d1(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[254, 192])).
% 0.37/0.54 tff(256,plain,
% 0.37/0.54 (d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[255, 165])).
% 0.37/0.54 tff(257,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(258,plain,
% 0.37/0.54 (((~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)))) <=> ((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(259,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[258])).
% 0.37/0.54 tff(260,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[259, 257])).
% 0.37/0.54 tff(261,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(262,plain,
% 0.37/0.54 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.37/0.54 tff(263,plain,
% 0.37/0.54 ((~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a3))) | c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[262, 108, 98])).
% 0.37/0.54 tff(264,plain,
% 0.37/0.54 (c(f(f(f(f(f(a3, a3), a3), f(a3, a3)), a3), f(f(f(a3, a3), a3), a3)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[263, 256])).
% 0.37/0.54 tff(265,plain,
% 0.37/0.54 (c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[264, 163])).
% 0.37/0.54 tff(266,plain,
% 0.37/0.54 (^[X: $i] : refl(((~c(X)) | (~d2(X))) <=> ((~c(X)) | (~d2(X))))),
% 0.37/0.54 inference(bind,[status(th)],[])).
% 0.37/0.54 tff(267,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d2(X))) <=> ![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.37/0.54 inference(quant_intro,[status(thm)],[266])).
% 0.37/0.54 tff(268,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d2(X))) <=> ![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(269,axiom,(![X: $i] : ((~c(X)) | (~d2(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','partitions_exclusive_c_d2')).
% 0.37/0.54 tff(270,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.37/0.54 tff(271,plain,(
% 0.37/0.54 ![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.37/0.54 inference(skolemize,[status(sab)],[270])).
% 0.37/0.54 tff(272,plain,
% 0.37/0.54 (![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.37/0.54 tff(273,plain,
% 0.37/0.54 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(274,plain,
% 0.37/0.55 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(275,plain,
% 0.37/0.55 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.37/0.55 tff(276,plain,
% 0.37/0.55 (~d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[275, 272, 265])).
% 0.37/0.55 tff(277,plain,
% 0.37/0.55 (~d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[276, 152])).
% 0.37/0.55 tff(278,plain,
% 0.37/0.55 (f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.37/0.55 inference(transitivity,[status(thm)],[148, 147, 144, 138, 136])).
% 0.37/0.55 tff(279,plain,
% 0.37/0.55 (d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) <=> d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[278])).
% 0.37/0.55 tff(280,plain,
% 0.37/0.55 (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))) <=> d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.55 inference(symmetry,[status(thm)],[279])).
% 0.37/0.55 tff(281,plain,
% 0.37/0.55 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.37/0.55 inference(symmetry,[status(thm)],[19])).
% 0.37/0.55 tff(282,plain,
% 0.37/0.55 (f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.37/0.55 inference(transitivity,[status(thm)],[51, 281])).
% 0.37/0.55 tff(283,plain,
% 0.37/0.55 (d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) <=> d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[282])).
% 0.37/0.55 tff(284,plain,
% 0.37/0.55 (d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) <=> d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.55 inference(transitivity,[status(thm)],[283, 280])).
% 0.37/0.55 tff(285,plain,
% 0.37/0.55 ((~d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) <=> (~d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[284])).
% 0.37/0.55 tff(286,plain,
% 0.37/0.55 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(287,plain,
% 0.37/0.55 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(288,plain,
% 0.37/0.55 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))) | (~d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.37/0.55 tff(289,plain,
% 0.37/0.55 (~d1(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[288, 207, 265])).
% 0.37/0.55 tff(290,plain,
% 0.37/0.55 (~d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.37/0.55 tff(291,plain,
% 0.37/0.55 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, a3)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(292,plain,
% 0.37/0.55 (((~d2(a3)) | c(f(a3, a3)) | (~d2(a3))) <=> ((~d2(a3)) | c(f(a3, a3)))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(293,plain,
% 0.37/0.55 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, a3))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[292])).
% 0.37/0.55 tff(294,plain,
% 0.37/0.55 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, a3)))),
% 0.37/0.55 inference(transitivity,[status(thm)],[293, 291])).
% 0.37/0.55 tff(295,plain,
% 0.37/0.55 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, a3)) | (~d2(a3)))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(296,plain,
% 0.37/0.55 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, a3))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.37/0.55 tff(297,plain,
% 0.37/0.55 (c(f(a3, a3))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[296, 184, 181])).
% 0.37/0.55 tff(298,plain,
% 0.37/0.55 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | (~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(299,plain,
% 0.37/0.55 (((~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) <=> ((~c(f(a3, a3))) | (~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(300,plain,
% 0.37/0.55 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))))),
% 0.37/0.55 inference(monotonicity,[status(thm)],[299])).
% 0.37/0.55 tff(301,plain,
% 0.37/0.55 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | (~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.55 inference(transitivity,[status(thm)],[300, 298])).
% 0.37/0.55 tff(302,plain,
% 0.37/0.55 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(303,plain,
% 0.37/0.55 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | (~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.37/0.56 tff(304,plain,
% 0.37/0.56 ((~c(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3))) | d1(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[303, 247, 297])).
% 0.37/0.56 tff(305,plain,
% 0.37/0.56 ($false),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[304, 290, 277, 133])).
% 0.37/0.56 tff(306,plain,(c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) | (~d1(f(f(a3, a3), f(a3, a3))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.56 tff(307,plain,
% 0.37/0.56 (c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[306, 97])).
% 0.37/0.56 tff(308,plain,
% 0.37/0.56 (f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)),
% 0.37/0.56 inference(transitivity,[status(thm)],[69, 67, 19, 14])).
% 0.37/0.56 tff(309,plain,
% 0.37/0.56 (d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) <=> d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[308])).
% 0.37/0.56 tff(310,assumption,(d1(f(f(f(a3, a3), a3), a3))), introduced(assumption)).
% 0.37/0.56 tff(311,plain,
% 0.37/0.56 (c(f(f(f(f(a3, a3), a3), a3), f(f(f(a3, a3), a3), a3)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[114, 108, 310])).
% 0.37/0.56 tff(312,plain,
% 0.37/0.56 (c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[311, 94])).
% 0.37/0.56 tff(313,plain,
% 0.37/0.56 (f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))),
% 0.37/0.56 inference(transitivity,[status(thm)],[69, 67])).
% 0.37/0.56 tff(314,plain,
% 0.37/0.56 (d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) <=> d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[313])).
% 0.37/0.56 tff(315,plain,
% 0.37/0.56 (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))) <=> d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.56 inference(symmetry,[status(thm)],[314])).
% 0.37/0.56 tff(316,plain,
% 0.37/0.56 ((~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))) <=> (~d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[315])).
% 0.37/0.56 tff(317,assumption,(~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))), introduced(assumption)).
% 0.37/0.56 tff(318,assumption,(c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))), introduced(assumption)).
% 0.37/0.56 tff(319,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(320,plain,
% 0.37/0.56 (((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) <=> (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(321,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[320])).
% 0.37/0.56 tff(322,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[321, 319])).
% 0.37/0.56 tff(323,plain,
% 0.37/0.56 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(324,plain,
% 0.37/0.56 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.37/0.56 tff(325,plain,
% 0.37/0.56 (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[324, 247])).
% 0.37/0.56 tff(326,plain,
% 0.37/0.56 (d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[325, 318, 317])).
% 0.37/0.56 tff(327,plain,
% 0.37/0.56 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(328,plain,
% 0.37/0.56 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(329,plain,
% 0.37/0.56 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.37/0.56 tff(330,plain,
% 0.37/0.56 (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[329, 272, 326])).
% 0.37/0.56 tff(331,plain,
% 0.37/0.56 (~c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[330, 130])).
% 0.37/0.56 tff(332,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(333,plain,
% 0.37/0.56 (((~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)))) <=> ((~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(334,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[333])).
% 0.37/0.56 tff(335,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[334, 332])).
% 0.37/0.56 tff(336,plain,
% 0.37/0.56 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(337,plain,
% 0.37/0.56 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.37/0.56 tff(338,plain,
% 0.37/0.56 (c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[337, 108, 310])).
% 0.37/0.56 tff(339,plain,
% 0.37/0.56 (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[338, 331])).
% 0.37/0.56 tff(340,plain,
% 0.37/0.56 (~d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[339, 316])).
% 0.37/0.56 tff(341,plain,
% 0.37/0.56 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(342,plain,
% 0.37/0.57 (((~c(f(a3, a3))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))) <=> ((~c(f(a3, a3))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(343,plain,
% 0.37/0.57 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[342])).
% 0.37/0.57 tff(344,plain,
% 0.37/0.57 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[343, 341])).
% 0.37/0.57 tff(345,plain,
% 0.37/0.57 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(346,plain,
% 0.37/0.57 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.37/0.57 tff(347,plain,
% 0.37/0.57 (d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3)))) | (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[346, 247, 297])).
% 0.37/0.57 tff(348,plain,
% 0.37/0.57 (d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[347, 340, 312])).
% 0.37/0.57 tff(349,plain,
% 0.37/0.57 (d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[348, 309])).
% 0.37/0.57 tff(350,plain,
% 0.37/0.57 (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[275, 272, 349])).
% 0.37/0.57 tff(351,plain,
% 0.37/0.57 (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[350, 50])).
% 0.37/0.57 tff(352,plain,
% 0.37/0.57 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3)))) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[166, 66])).
% 0.37/0.57 tff(353,plain,
% 0.37/0.57 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3)))) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(354,plain,
% 0.37/0.57 (f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3)))) = f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[353, 7])).
% 0.37/0.57 tff(355,plain,
% 0.37/0.57 (f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.57 inference(symmetry,[status(thm)],[354])).
% 0.37/0.57 tff(356,plain,
% 0.37/0.57 (f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[355, 352])).
% 0.37/0.57 tff(357,plain,
% 0.37/0.57 (c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))) <=> c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[356])).
% 0.37/0.57 tff(358,plain,
% 0.37/0.57 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) <=> c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.57 inference(symmetry,[status(thm)],[357])).
% 0.37/0.57 tff(359,plain,
% 0.37/0.57 ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) <=> (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[358])).
% 0.37/0.57 tff(360,plain,
% 0.37/0.57 (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[330, 359])).
% 0.37/0.57 tff(361,plain,
% 0.37/0.57 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[318, 168])).
% 0.37/0.57 tff(362,plain,
% 0.37/0.57 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(363,plain,
% 0.37/0.57 (((~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(a3))) <=> ((~d2(a3)) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(364,plain,
% 0.37/0.57 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[363])).
% 0.37/0.57 tff(365,plain,
% 0.37/0.57 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(a3)))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[364, 362])).
% 0.37/0.58 tff(366,plain,
% 0.37/0.58 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(a3)))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(367,plain,
% 0.37/0.58 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.37/0.58 tff(368,plain,
% 0.37/0.58 (c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3)) | (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[367, 184, 181])).
% 0.37/0.58 tff(369,plain,
% 0.37/0.58 (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[368, 350])).
% 0.37/0.58 tff(370,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(371,plain,
% 0.37/0.58 (((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) <=> ((~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(372,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[371])).
% 0.37/0.58 tff(373,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[372, 370])).
% 0.37/0.58 tff(374,plain,
% 0.37/0.58 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(375,plain,
% 0.37/0.58 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.37/0.58 tff(376,plain,
% 0.37/0.58 (d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[375, 247, 297])).
% 0.37/0.58 tff(377,plain,
% 0.37/0.58 (d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[376, 369, 361])).
% 0.37/0.58 tff(378,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(379,plain,
% 0.37/0.58 (((~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))) <=> ((~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(380,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[379])).
% 0.37/0.58 tff(381,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[380, 378])).
% 0.37/0.58 tff(382,plain,
% 0.37/0.58 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(383,plain,
% 0.37/0.58 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.37/0.58 tff(384,plain,
% 0.37/0.58 ((~d1(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))) | c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[383, 108])).
% 0.37/0.58 tff(385,plain,
% 0.37/0.58 (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[384, 377, 360])).
% 0.37/0.58 tff(386,plain,
% 0.37/0.58 (d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) <=> d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[41])).
% 0.37/0.58 tff(387,plain,
% 0.37/0.58 (d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) <=> d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))),
% 0.37/0.58 inference(symmetry,[status(thm)],[386])).
% 0.37/0.58 tff(388,plain,
% 0.37/0.58 ((~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) <=> (~d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[387])).
% 0.37/0.58 tff(389,plain,
% 0.37/0.58 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(390,plain,
% 0.37/0.58 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(391,plain,
% 0.37/0.58 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.37/0.58 tff(392,plain,
% 0.37/0.58 (~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[391, 207, 318])).
% 0.37/0.58 tff(393,plain,
% 0.37/0.58 (~d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.37/0.58 tff(394,plain,
% 0.37/0.58 (d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) <=> d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[41])).
% 0.37/0.58 tff(395,plain,
% 0.37/0.58 (d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))) <=> d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))),
% 0.37/0.58 inference(symmetry,[status(thm)],[394])).
% 0.37/0.58 tff(396,plain,
% 0.37/0.58 ((~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) <=> (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[395])).
% 0.37/0.58 tff(397,plain,
% 0.37/0.58 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(398,plain,
% 0.37/0.58 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(399,plain,
% 0.37/0.58 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.37/0.58 tff(400,plain,
% 0.37/0.58 (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[399, 272, 318])).
% 0.37/0.58 tff(401,plain,
% 0.37/0.58 (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[400, 396])).
% 0.37/0.58 tff(402,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(403,plain,
% 0.37/0.58 (((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))) <=> ((~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(404,plain,
% 0.37/0.58 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[403])).
% 0.37/0.59 tff(405,plain,
% 0.37/0.59 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[404, 402])).
% 0.37/0.59 tff(406,plain,
% 0.37/0.59 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(407,plain,
% 0.37/0.59 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.37/0.59 tff(408,plain,
% 0.37/0.59 (d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3))) | (~c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[407, 247, 297])).
% 0.37/0.59 tff(409,plain,
% 0.37/0.59 (~c(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[408, 401, 393])).
% 0.37/0.59 tff(410,plain,
% 0.37/0.59 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(411,plain,
% 0.37/0.59 ((d2(f(f(a3, f(a3, a3)), f(a3, a3))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3)))) <=> (d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(412,plain,
% 0.37/0.59 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a3, f(a3, a3)), f(a3, a3))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[411])).
% 0.37/0.59 tff(413,plain,
% 0.37/0.59 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a3, f(a3, a3)), f(a3, a3))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[412, 410])).
% 0.37/0.59 tff(414,plain,
% 0.37/0.59 ((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a3, f(a3, a3)), f(a3, a3))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(415,plain,
% 0.37/0.59 ((~![X: $i] : (d2(X) | d1(X) | c(X))) | d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3))) | c(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.37/0.59 tff(416,plain,
% 0.37/0.59 (d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[415, 229, 409])).
% 0.37/0.59 tff(417,plain,
% 0.37/0.59 (d2(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[416, 385])).
% 0.37/0.59 tff(418,plain,
% 0.37/0.59 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(419,plain,
% 0.37/0.59 (((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3))))) <=> ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(420,plain,
% 0.37/0.59 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[419])).
% 0.37/0.59 tff(421,plain,
% 0.37/0.59 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[420, 418])).
% 0.37/0.59 tff(422,plain,
% 0.37/0.59 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(423,plain,
% 0.37/0.59 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.37/0.59 tff(424,plain,
% 0.37/0.59 ((~d2(f(f(a3, f(a3, a3)), f(a3, a3)))) | c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[423, 181])).
% 0.37/0.59 tff(425,plain,
% 0.37/0.59 (c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[424, 417])).
% 0.37/0.59 tff(426,plain,
% 0.37/0.59 ($false),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[425, 351])).
% 0.37/0.59 tff(427,plain,((~c(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))) | (~d1(f(f(f(a3, a3), a3), a3))) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.59 tff(428,plain,
% 0.37/0.59 (d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[427, 307, 98])).
% 0.37/0.59 tff(429,plain,
% 0.37/0.59 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(430,plain,
% 0.37/0.59 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(431,plain,
% 0.37/0.59 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.37/0.59 tff(432,plain,
% 0.37/0.59 (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[431, 207, 428])).
% 0.37/0.59 tff(433,plain,
% 0.37/0.59 (~c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[432, 130])).
% 0.37/0.59 tff(434,plain,
% 0.37/0.59 (c(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)), f(f(f(a3, a3), a3), a3))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[337, 108, 98])).
% 0.37/0.59 tff(435,plain,
% 0.37/0.59 (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))), f(f(a3, a3), a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[434, 433])).
% 0.37/0.59 tff(436,plain,
% 0.37/0.59 (~d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(f(a3, a3), a3)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[435, 121])).
% 0.37/0.59 tff(437,plain,
% 0.37/0.59 (~d1(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[436, 119])).
% 0.37/0.59 tff(438,plain,
% 0.37/0.59 (d2(f(f(a3, a3), f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, a3), a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[347, 437, 116])).
% 0.37/0.59 tff(439,plain,
% 0.37/0.59 (d2(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[438, 72])).
% 0.37/0.59 tff(440,plain,
% 0.37/0.59 (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), a3))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[275, 272, 439])).
% 0.37/0.59 tff(441,plain,
% 0.37/0.59 (~c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[440, 50])).
% 0.37/0.59 tff(442,plain,
% 0.37/0.59 (~c(f(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[432, 359])).
% 0.37/0.59 tff(443,plain,
% 0.37/0.59 (~d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[368, 440])).
% 0.37/0.59 tff(444,plain,
% 0.37/0.59 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[307, 168])).
% 0.37/0.59 tff(445,plain,
% 0.37/0.59 (d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3))) | d2(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[375, 247, 297, 444])).
% 0.37/0.59 tff(446,plain,
% 0.37/0.59 (d1(f(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a3), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[445, 443])).
% 0.37/0.59 tff(447,plain,
% 0.37/0.59 (~d1(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[384, 446, 442])).
% 0.37/0.59 tff(448,plain,
% 0.37/0.59 (~d1(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[391, 207, 307])).
% 0.37/0.59 tff(449,plain,
% 0.37/0.59 (~d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[448, 388])).
% 0.37/0.59 tff(450,plain,
% 0.37/0.59 (~d2(f(f(f(a3, a3), a3), f(f(a3, a3), f(a3, a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[399, 272, 307])).
% 0.37/0.59 tff(451,plain,
% 0.37/0.59 (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[450, 396])).
% 0.37/0.59 tff(452,plain,
% 0.37/0.59 (~c(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[408, 451, 449])).
% 0.37/0.59 tff(453,plain,
% 0.37/0.59 (d1(f(f(a3, f(a3, a3)), f(a3, a3))) | d2(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[415, 229, 452])).
% 0.37/0.59 tff(454,plain,
% 0.37/0.59 (d2(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[453, 447])).
% 0.37/0.59 tff(455,plain,
% 0.37/0.59 (c(f(f(f(a3, f(a3, a3)), f(a3, a3)), f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[424, 454])).
% 0.37/0.59 tff(456,plain,
% 0.37/0.59 ($false),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[455, 441])).
% 0.37/0.59 tff(457,plain,(~d1(f(f(a3, a3), f(a3, a3)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.59 tff(458,plain,
% 0.37/0.59 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(459,plain,
% 0.37/0.59 (((~c(f(a3, a3))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3)))) <=> ((~c(f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(460,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[459])).
% 0.37/0.60 tff(461,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[460, 458])).
% 0.37/0.60 tff(462,plain,
% 0.37/0.60 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(463,plain,
% 0.37/0.60 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.37/0.60 tff(464,plain,
% 0.37/0.60 (d2(f(f(a3, a3), f(a3, a3))) | d1(f(f(a3, a3), f(a3, a3)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[463, 247, 297])).
% 0.37/0.60 tff(465,plain,
% 0.37/0.60 (d2(f(f(a3, a3), f(a3, a3)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[464, 457])).
% 0.37/0.60 tff(466,plain,
% 0.37/0.60 (d2(f(f(f(a3, a3), a3), a3))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[465, 12])).
% 0.37/0.60 tff(467,plain,
% 0.37/0.60 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(468,plain,
% 0.37/0.60 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(469,plain,
% 0.37/0.60 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.37/0.60 tff(470,plain,
% 0.37/0.60 (~c(f(f(f(a3, a3), a3), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[469, 272, 466])).
% 0.37/0.60 tff(471,plain,
% 0.37/0.60 (~d2(f(f(a3, a3), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[218, 470])).
% 0.37/0.60 tff(472,plain,
% 0.37/0.60 (f(f(f(a3, a3), a3), f(a3, a3)) = f(f(a3, f(a3, a3)), f(a3, a3))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[80])).
% 0.37/0.60 tff(473,plain,
% 0.37/0.60 (f(f(a3, f(a3, a3)), f(a3, a3)) = f(f(f(a3, a3), a3), f(a3, a3))),
% 0.37/0.60 inference(symmetry,[status(thm)],[472])).
% 0.37/0.60 tff(474,assumption,(f(a3, f(f(a3, a3), f(a3, a3))) = f(f(a3, f(a3, a3)), f(a3, a3))), introduced(assumption)).
% 0.37/0.60 tff(475,plain,
% 0.37/0.60 (f(a3, f(f(a3, a3), f(a3, a3))) = f(a3, f(f(f(a3, a3), a3), a3))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[9])).
% 0.37/0.60 tff(476,plain,
% 0.37/0.60 (f(a3, f(f(f(a3, a3), a3), a3)) = f(a3, f(f(a3, a3), f(a3, a3)))),
% 0.37/0.60 inference(symmetry,[status(thm)],[475])).
% 0.37/0.60 tff(477,plain,
% 0.37/0.60 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a3, f(f(f(a3, a3), a3), a3)) = f(f(a3, f(f(a3, a3), a3)), a3))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(478,plain,
% 0.37/0.60 (f(a3, f(f(f(a3, a3), a3), a3)) = f(f(a3, f(f(a3, a3), a3)), a3)),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[477, 7])).
% 0.37/0.60 tff(479,plain,
% 0.37/0.60 (f(f(a3, f(f(a3, a3), a3)), a3) = f(a3, f(f(f(a3, a3), a3), a3))),
% 0.37/0.60 inference(symmetry,[status(thm)],[478])).
% 0.37/0.60 tff(480,plain,
% 0.37/0.60 (f(f(a3, f(f(a3, a3), a3)), a3) = f(f(f(a3, a3), a3), f(a3, a3))),
% 0.37/0.60 inference(transitivity,[status(thm)],[479, 476, 474, 473])).
% 0.37/0.60 tff(481,plain,
% 0.37/0.60 (d2(f(f(a3, f(f(a3, a3), a3)), a3)) <=> d2(f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[480])).
% 0.37/0.60 tff(482,plain,
% 0.37/0.60 ((~d2(f(f(a3, f(f(a3, a3), a3)), a3))) <=> (~d2(f(f(f(a3, a3), a3), f(a3, a3))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[481])).
% 0.37/0.60 tff(483,plain,
% 0.37/0.60 (c(f(f(a3, f(f(a3, a3), a3)), a3)) <=> c(f(a3, f(f(f(a3, a3), a3), a3)))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[479])).
% 0.37/0.60 tff(484,plain,
% 0.37/0.60 (c(f(a3, f(f(f(a3, a3), a3), a3))) <=> c(f(f(a3, f(f(a3, a3), a3)), a3))),
% 0.37/0.60 inference(symmetry,[status(thm)],[483])).
% 0.37/0.60 tff(485,assumption,(d2(f(f(a3, a3), f(a3, a3)))), introduced(assumption)).
% 0.37/0.60 tff(486,plain,
% 0.37/0.60 (d2(f(f(f(a3, a3), a3), a3))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[485, 12])).
% 0.37/0.60 tff(487,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(488,plain,
% 0.37/0.60 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(489,plain,
% 0.37/0.60 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.37/0.60 tff(490,plain,
% 0.37/0.60 (c(f(a3, f(f(f(a3, a3), a3), a3))) | (~d2(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[489, 184, 181])).
% 0.37/0.60 tff(491,plain,
% 0.37/0.60 (c(f(a3, f(f(f(a3, a3), a3), a3)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[490, 486])).
% 0.37/0.60 tff(492,plain,
% 0.37/0.60 (c(f(f(a3, f(f(a3, a3), a3)), a3))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[491, 484])).
% 0.37/0.60 tff(493,plain,
% 0.37/0.60 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d2(f(f(a3, f(f(a3, a3), a3)), a3))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d2(f(f(a3, f(f(a3, a3), a3)), a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(494,plain,
% 0.37/0.60 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d2(f(f(a3, f(f(a3, a3), a3)), a3))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(495,plain,
% 0.37/0.60 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d2(f(f(a3, f(f(a3, a3), a3)), a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.37/0.60 tff(496,plain,
% 0.37/0.60 (~d2(f(f(a3, f(f(a3, a3), a3)), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[495, 272, 492])).
% 0.37/0.60 tff(497,plain,
% 0.37/0.60 (~d2(f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[496, 482])).
% 0.37/0.60 tff(498,plain,
% 0.37/0.60 (d1(f(f(a3, f(f(a3, a3), a3)), a3)) <=> d1(f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[480])).
% 0.37/0.60 tff(499,plain,
% 0.37/0.60 ((~d1(f(f(a3, f(f(a3, a3), a3)), a3))) <=> (~d1(f(f(f(a3, a3), a3), f(a3, a3))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[498])).
% 0.37/0.60 tff(500,plain,
% 0.37/0.60 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d1(f(f(a3, f(f(a3, a3), a3)), a3))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d1(f(f(a3, f(f(a3, a3), a3)), a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(501,plain,
% 0.37/0.60 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d1(f(f(a3, f(f(a3, a3), a3)), a3))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(502,plain,
% 0.37/0.60 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(a3, f(f(a3, a3), a3)), a3))) | (~d1(f(f(a3, f(f(a3, a3), a3)), a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.37/0.60 tff(503,plain,
% 0.37/0.60 (~d1(f(f(a3, f(f(a3, a3), a3)), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[502, 207, 492])).
% 0.37/0.60 tff(504,plain,
% 0.37/0.60 (~d1(f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[503, 499])).
% 0.37/0.60 tff(505,assumption,(c(f(f(a3, a3), a3))), introduced(assumption)).
% 0.37/0.60 tff(506,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(507,plain,
% 0.37/0.60 (((~c(f(f(a3, a3), a3))) | (~c(f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3)))) <=> ((~c(f(a3, a3))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(508,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | (~c(f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3)))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[507])).
% 0.37/0.60 tff(509,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | (~c(f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[508, 506])).
% 0.37/0.60 tff(510,plain,
% 0.37/0.60 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, a3), a3))) | (~c(f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(511,plain,
% 0.37/0.60 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(a3, a3))) | (~c(f(f(a3, a3), a3))) | d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.37/0.60 tff(512,plain,
% 0.37/0.60 (d2(f(f(f(a3, a3), a3), f(a3, a3))) | d1(f(f(f(a3, a3), a3), f(a3, a3)))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[511, 247, 297, 505])).
% 0.37/0.60 tff(513,plain,
% 0.37/0.60 ($false),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[512, 504, 497])).
% 0.37/0.60 tff(514,plain,((~(f(a3, f(f(a3, a3), f(a3, a3))) = f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(f(f(a3, a3), a3))) | (~d2(f(f(a3, a3), f(a3, a3))))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.60 tff(515,plain,
% 0.37/0.60 ((~c(f(f(a3, a3), a3))) | (~d2(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[514, 62])).
% 0.37/0.60 tff(516,plain,
% 0.37/0.60 (~c(f(f(a3, a3), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[515, 465])).
% 0.37/0.60 tff(517,plain,
% 0.37/0.60 (d1(f(f(a3, a3), a3)) | d2(f(f(a3, a3), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[235, 229, 516])).
% 0.37/0.60 tff(518,plain,
% 0.37/0.60 (d1(f(f(a3, a3), a3))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[517, 471])).
% 0.37/0.60 tff(519,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(520,plain,
% 0.37/0.60 (((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) <=> ((~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(521,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[520])).
% 0.37/0.60 tff(522,plain,
% 0.37/0.60 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[521, 519])).
% 0.37/0.60 tff(523,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(524,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, a3), a3))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.37/0.61 tff(525,plain,
% 0.37/0.61 (c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[524, 108, 518])).
% 0.37/0.61 tff(526,plain,
% 0.37/0.61 (f(f(a3, f(a3, a3)), f(f(a3, a3), a3)) = f(f(f(a3, a3), a3), f(f(a3, a3), a3))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[26])).
% 0.37/0.61 tff(527,plain,
% 0.37/0.61 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a3, f(f(a3, a3), f(f(a3, a3), a3))) = f(f(a3, f(a3, a3)), f(f(a3, a3), a3)))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(528,plain,
% 0.37/0.61 (f(a3, f(f(a3, a3), f(f(a3, a3), a3))) = f(f(a3, f(a3, a3)), f(f(a3, a3), a3))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[527, 7])).
% 0.37/0.61 tff(529,plain,
% 0.37/0.61 (f(a3, f(f(a3, f(a3, a3)), f(a3, a3))) = f(a3, f(f(a3, a3), f(f(a3, a3), a3)))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[45])).
% 0.37/0.61 tff(530,plain,
% 0.37/0.61 (f(a3, f(f(a3, f(a3, a3)), f(a3, a3))) = f(f(f(a3, a3), a3), f(f(a3, a3), a3))),
% 0.37/0.61 inference(transitivity,[status(thm)],[529, 528, 526])).
% 0.37/0.61 tff(531,plain,
% 0.37/0.61 (f(f(a3, f(f(a3, f(a3, a3)), f(a3, a3))), a1) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)),
% 0.37/0.61 inference(monotonicity,[status(thm)],[530])).
% 0.37/0.61 tff(532,plain,
% 0.37/0.61 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) = f(f(a3, f(f(a3, f(a3, a3)), f(a3, a3))), a1))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(533,plain,
% 0.37/0.61 (f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) = f(f(a3, f(f(a3, f(a3, a3)), f(a3, a3))), a1)),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[532, 7])).
% 0.37/0.61 tff(534,plain,
% 0.37/0.61 (f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)),
% 0.37/0.61 inference(transitivity,[status(thm)],[533, 531])).
% 0.37/0.61 tff(535,plain,
% 0.37/0.61 (c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) <=> c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[534])).
% 0.37/0.61 tff(536,plain,
% 0.37/0.61 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) <=> c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))),
% 0.37/0.61 inference(symmetry,[status(thm)],[535])).
% 0.37/0.61 tff(537,plain,
% 0.37/0.61 ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) <=> (~c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[536])).
% 0.37/0.61 tff(538,assumption,(~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))), introduced(assumption)).
% 0.37/0.61 tff(539,plain,
% 0.37/0.61 (~c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.37/0.61 tff(540,plain,
% 0.37/0.61 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) | (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) | (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(541,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) | (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(542,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) | (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.37/0.61 tff(543,plain,
% 0.37/0.61 (c(f(a3, f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) | (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[542, 184, 181])).
% 0.37/0.61 tff(544,plain,
% 0.37/0.61 (~d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[543, 539])).
% 0.37/0.61 tff(545,plain,
% 0.37/0.61 (c(f(f(a3, f(a3, a3)), f(a3, a3))) <=> c(f(a3, f(f(a3, a3), f(a3, a3))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[63])).
% 0.37/0.61 tff(546,plain,
% 0.37/0.61 (c(f(a3, f(f(a3, a3), f(a3, a3)))) <=> c(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.61 inference(symmetry,[status(thm)],[545])).
% 0.37/0.61 tff(547,plain,
% 0.37/0.61 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, f(f(a3, a3), f(a3, a3)))) | (~d2(f(f(a3, a3), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, f(f(a3, a3), f(a3, a3)))) | (~d2(f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(548,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(a3)) | c(f(a3, f(f(a3, a3), f(a3, a3)))) | (~d2(f(f(a3, a3), f(a3, a3)))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(549,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(a3)) | c(f(a3, f(f(a3, a3), f(a3, a3)))) | (~d2(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.37/0.61 tff(550,plain,
% 0.37/0.61 (c(f(a3, f(f(a3, a3), f(a3, a3)))) | (~d2(f(f(a3, a3), f(a3, a3))))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[549, 184, 181])).
% 0.37/0.61 tff(551,plain,
% 0.37/0.61 (c(f(a3, f(f(a3, a3), f(a3, a3))))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[550, 465])).
% 0.37/0.61 tff(552,plain,
% 0.37/0.61 (c(f(f(a3, f(a3, a3)), f(a3, a3)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[551, 546])).
% 0.37/0.61 tff(553,plain,
% 0.37/0.61 (c(a1) <=> c(a1)),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(554,axiom,(c(a1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','partition_c_not_empty')).
% 0.37/0.61 tff(555,plain,
% 0.37/0.61 (c(a1)),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.37/0.61 tff(556,plain,
% 0.37/0.61 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(557,plain,
% 0.37/0.61 (((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))) <=> ((~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(558,plain,
% 0.37/0.61 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | (~c(f(f(a3, f(a3, a3)), f(a3, a3))))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[557])).
% 0.37/0.61 tff(559,plain,
% 0.37/0.61 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | (~c(f(f(a3, f(a3, a3)), f(a3, a3)))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[558, 556])).
% 0.37/0.61 tff(560,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a3, f(a3, a3)), f(a3, a3)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(561,plain,
% 0.37/0.61 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | (~c(f(f(a3, f(a3, a3)), f(a3, a3))))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.37/0.61 tff(562,plain,
% 0.37/0.61 (d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) | d2(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[561, 555, 247, 552])).
% 0.37/0.61 tff(563,plain,
% 0.37/0.61 (d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[562, 544])).
% 0.37/0.61 tff(564,plain,
% 0.37/0.61 (f(f(f(a3, f(a3, a3)), f(a3, a3)), a1) = f(f(f(f(a3, a3), a3), f(a3, a3)), a1)),
% 0.37/0.61 inference(monotonicity,[status(thm)],[39])).
% 0.37/0.61 tff(565,plain,
% 0.37/0.61 (f(f(f(f(a3, a3), a3), f(a3, a3)), a1) = f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)),
% 0.37/0.61 inference(symmetry,[status(thm)],[564])).
% 0.37/0.61 tff(566,plain,
% 0.37/0.61 (d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1)) <=> d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[565])).
% 0.37/0.61 tff(567,plain,
% 0.37/0.61 (d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)) <=> d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))),
% 0.37/0.61 inference(symmetry,[status(thm)],[566])).
% 0.37/0.61 tff(568,assumption,(d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1))), introduced(assumption)).
% 0.37/0.61 tff(569,plain,
% 0.37/0.61 (d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.37/0.61 tff(570,assumption,(c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))), introduced(assumption)).
% 0.37/0.61 tff(571,plain,
% 0.37/0.61 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(572,plain,
% 0.37/0.61 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(573,plain,
% 0.37/0.61 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(a3, a3)), a1)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.37/0.61 tff(574,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[573, 207, 570, 569])).
% 0.37/0.61 tff(575,plain,((~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))) | (~d1(f(f(f(a3, f(a3, a3)), f(a3, a3)), a1)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(576,plain,
% 0.37/0.61 (~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[575, 563])).
% 0.37/0.61 tff(577,plain,
% 0.37/0.61 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a3, a3), a3), f(f(a3, a3), a1)) = f(f(f(f(a3, a3), a3), f(a3, a3)), a1))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(578,plain,
% 0.37/0.61 (f(f(f(a3, a3), a3), f(f(a3, a3), a1)) = f(f(f(f(a3, a3), a3), f(a3, a3)), a1)),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[577, 7])).
% 0.37/0.61 tff(579,plain,
% 0.37/0.61 (c(f(f(f(a3, a3), a3), f(f(a3, a3), a1))) <=> c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[578])).
% 0.37/0.61 tff(580,plain,
% 0.37/0.61 (c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1)) <=> c(f(f(f(a3, a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.61 inference(symmetry,[status(thm)],[579])).
% 0.37/0.61 tff(581,plain,
% 0.37/0.61 ((~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))) <=> (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a1))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[580])).
% 0.37/0.61 tff(582,assumption,(~c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))), introduced(assumption)).
% 0.37/0.61 tff(583,plain,
% 0.37/0.61 (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.61 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.37/0.61 tff(584,assumption,(c(f(f(f(a3, a3), a3), f(f(a3, a3), a1)))), introduced(assumption)).
% 0.37/0.61 tff(585,plain,
% 0.37/0.61 ($false),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[584, 583])).
% 0.37/0.61 tff(586,plain,((~c(f(f(f(a3, a3), a3), f(f(a3, a3), a1)))) | c(f(f(f(f(a3, a3), a3), f(a3, a3)), a1))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.61 tff(587,plain,
% 0.37/0.61 (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.61 inference(unit_resolution,[status(thm)],[586, 576])).
% 0.37/0.61 tff(588,plain,
% 0.37/0.61 (f(f(f(f(f(a3, a3), a3), a3), f(a3, a3)), a1) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)),
% 0.37/0.61 inference(monotonicity,[status(thm)],[143])).
% 0.37/0.61 tff(589,plain,
% 0.37/0.61 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1)) = f(f(f(f(f(a3, a3), a3), a3), f(a3, a3)), a1))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(590,plain,
% 0.37/0.62 (f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1)) = f(f(f(f(f(a3, a3), a3), a3), f(a3, a3)), a1)),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[589, 7])).
% 0.37/0.62 tff(591,plain,
% 0.37/0.62 (f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1)) = f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)),
% 0.37/0.62 inference(transitivity,[status(thm)],[590, 588])).
% 0.37/0.62 tff(592,plain,
% 0.37/0.62 (c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) <=> c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[591])).
% 0.37/0.62 tff(593,plain,
% 0.37/0.62 (c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) <=> c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.62 inference(symmetry,[status(thm)],[592])).
% 0.37/0.62 tff(594,plain,
% 0.37/0.62 ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) <=> (~c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[593])).
% 0.37/0.62 tff(595,plain,
% 0.37/0.62 (~c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[538, 594])).
% 0.37/0.62 tff(596,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(f(a3, a3), a3), a3))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(597,plain,
% 0.37/0.62 (((~d2(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(a3, a3), a1)))) <=> ((~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(598,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(a3, a3), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(f(a3, a3), a3), a3)))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[597])).
% 0.37/0.62 tff(599,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(a3, a3), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(f(a3, a3), a3), a3))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[598, 596])).
% 0.37/0.62 tff(600,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(a3, a3), a3), a3))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(a3, a3), a1))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(601,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1))) | (~d2(f(f(f(a3, a3), a3), a3)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.37/0.62 tff(602,plain,
% 0.37/0.62 ((~d2(f(f(a3, a3), a1))) | c(f(f(f(f(a3, a3), a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[601, 181, 466])).
% 0.37/0.62 tff(603,plain,
% 0.37/0.62 (~d2(f(f(a3, a3), a1))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[602, 595])).
% 0.37/0.62 tff(604,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(f(a3, a3))) | d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(a3, a3))) | d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1)))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(605,plain,
% 0.37/0.62 (((~c(f(a3, a3))) | (~c(a1)) | d1(f(f(a3, a3), a1)) | d2(f(f(a3, a3), a1))) <=> ((~c(a1)) | (~c(f(a3, a3))) | d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1)))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(606,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(a1)) | d1(f(f(a3, a3), a1)) | d2(f(f(a3, a3), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(f(a3, a3))) | d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[605])).
% 0.37/0.62 tff(607,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(a1)) | d1(f(f(a3, a3), a1)) | d2(f(f(a3, a3), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(a3, a3))) | d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1)))),
% 0.37/0.62 inference(transitivity,[status(thm)],[606, 604])).
% 0.37/0.62 tff(608,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(a3, a3))) | (~c(a1)) | d1(f(f(a3, a3), a1)) | d2(f(f(a3, a3), a1)))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(609,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(a3, a3))) | d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.37/0.62 tff(610,plain,
% 0.37/0.62 (d2(f(f(a3, a3), a1)) | d1(f(f(a3, a3), a1))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[609, 555, 247, 297])).
% 0.37/0.62 tff(611,plain,
% 0.37/0.62 (d1(f(f(a3, a3), a1))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[610, 603])).
% 0.37/0.62 tff(612,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a1))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a1))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a1))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(613,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a1))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a1))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(614,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a3, a3), a3))) | (~d1(f(f(a3, a3), a1))) | c(f(f(f(a3, a3), a3), f(f(a3, a3), a1)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.37/0.62 tff(615,plain,
% 0.37/0.62 ($false),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[614, 108, 518, 611, 587])).
% 0.37/0.62 tff(616,plain,(c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.62 tff(617,plain,
% 0.37/0.62 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(618,plain,
% 0.37/0.62 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(619,plain,
% 0.37/0.62 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.37/0.62 tff(620,plain,
% 0.37/0.62 (~d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[619, 272, 616])).
% 0.37/0.62 tff(621,plain,
% 0.37/0.62 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(622,plain,
% 0.37/0.62 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(623,plain,
% 0.37/0.62 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) | (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.37/0.62 tff(624,plain,
% 0.37/0.62 (~d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[623, 207, 616])).
% 0.37/0.62 tff(625,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(626,plain,
% 0.37/0.62 (((~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | (~c(a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1))) <=> ((~c(a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(627,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | (~c(a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))))),
% 0.37/0.62 inference(monotonicity,[status(thm)],[626])).
% 0.37/0.62 tff(628,plain,
% 0.37/0.62 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | (~c(a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))))),
% 0.37/0.62 inference(transitivity,[status(thm)],[627, 625])).
% 0.37/0.62 tff(629,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3)))) | (~c(a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(630,plain,
% 0.37/0.62 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.37/0.62 tff(631,plain,
% 0.37/0.62 (d2(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | d1(f(f(f(f(a3, a3), a3), f(f(a3, a3), a3)), a1)) | (~c(f(f(f(a3, a3), a3), f(f(a3, a3), a3))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[630, 555, 247])).
% 0.37/0.62 tff(632,plain,
% 0.37/0.62 ($false),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[631, 624, 620, 525])).
% 0.37/0.62 % SZS output end Proof
% 0.37/0.62 % E exiting
%------------------------------------------------------------------------------