%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET620+3 : TPTP v9.0.0. Released v2.2.0.
% 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 05:26:01 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET620+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:31:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(difference_type, type, (
% 0.19/0.37 difference: ( $i * $i ) > $i)).
% 0.19/0.37 tff(intersection_type, type, (
% 0.19/0.37 intersection: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_C_2_type, type, (
% 0.19/0.37 tptp_fun_C_2: $i)).
% 0.19/0.37 tff(tptp_fun_B_3_type, type, (
% 0.19/0.37 tptp_fun_B_3: $i)).
% 0.19/0.37 tff(union_type, type, (
% 0.19/0.37 union: ( $i * $i ) > $i)).
% 0.19/0.37 tff(symmetric_difference_type, type, (
% 0.19/0.37 symmetric_difference: ( $i * $i ) > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[B: $i, C: $i, D: $i] : refl((difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> (difference(union(B, C), D) = union(difference(B, D), difference(C, D))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,axiom,(![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_distributes_over_union')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))) | (difference(union(B!3, C!2), intersection(B!3, C!2)) = union(difference(B!3, intersection(B!3, C!2)), difference(C!2, intersection(B!3, C!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (difference(union(B!3, C!2), intersection(B!3, C!2)) = union(difference(B!3, intersection(B!3, C!2)), difference(C!2, intersection(B!3, C!2)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (union(difference(B!3, intersection(B!3, C!2)), difference(C!2, intersection(B!3, C!2))) = difference(union(B!3, C!2), intersection(B!3, C!2))),
% 0.19/0.37 inference(symmetry,[status(thm)],[9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(14,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.37 tff(16,plain,(
% 0.19/0.37 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(skolemize,[status(sab)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!2, B!3) = intersection(B!3, C!2))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.19/0.37 inference(symmetry,[status(thm)],[19])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (difference(C!2, intersection(B!3, C!2)) = difference(C!2, intersection(C!2, B!3))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (difference(C!2, intersection(C!2, B!3)) = difference(C!2, intersection(B!3, C!2))),
% 0.19/0.37 inference(symmetry,[status(thm)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (^[B: $i, C: $i] : refl((difference(B, intersection(B, C)) = difference(B, C)) <=> (difference(B, intersection(B, C)) = difference(B, C)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C)) <=> ![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C)) <=> ![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(26,axiom,(![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_into_intersection')).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,(
% 0.19/0.37 ![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.19/0.37 inference(skolemize,[status(sab)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))) | (difference(C!2, intersection(C!2, B!3)) = difference(C!2, B!3))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (difference(C!2, intersection(C!2, B!3)) = difference(C!2, B!3)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (difference(C!2, B!3) = difference(C!2, intersection(C!2, B!3))),
% 0.19/0.37 inference(symmetry,[status(thm)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (difference(C!2, B!3) = difference(C!2, intersection(B!3, C!2))),
% 0.19/0.37 inference(transitivity,[status(thm)],[32, 22])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))) | (difference(B!3, intersection(B!3, C!2)) = difference(B!3, C!2))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (difference(B!3, intersection(B!3, C!2)) = difference(B!3, C!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))),
% 0.19/0.37 inference(symmetry,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (union(difference(B!3, C!2), difference(C!2, B!3)) = union(difference(B!3, intersection(B!3, C!2)), difference(C!2, intersection(B!3, C!2)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[36, 33])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(41,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.37 tff(43,plain,(
% 0.19/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[42])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!3, C!2) = union(difference(B!3, C!2), difference(C!2, B!3)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (symmetric_difference(B!3, C!2) = union(difference(B!3, C!2), difference(C!2, B!3))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (symmetric_difference(B!3, C!2) = difference(union(B!3, C!2), intersection(B!3, C!2))),
% 0.19/0.37 inference(transitivity,[status(thm)],[46, 37, 10])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))) <=> (~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(49,axiom,(~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th96')).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[50, 48])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (~![B: $i, C: $i] : (symmetric_difference(B, C) = difference(union(B, C), intersection(B, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.37 tff(54,plain,(
% 0.19/0.37 ~(symmetric_difference(B!3, C!2) = difference(union(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[53])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[54, 47])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------