%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW962+1 : TPTP v9.0.0. Released v7.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:37:43 AM UTC 2025
% Result : Theorem 0.77s 0.95s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW962+1 : TPTP v9.0.0. Released v7.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:14:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.77/0.95 % SZS status Theorem
% 0.77/0.95 % SZS output start Proof
% 0.77/0.95 tff(pred_attacker_type, type, (
% 0.77/0.95 pred_attacker: $i > $o)).
% 0.77/0.95 tff(constr_CONST_1_type, type, (
% 0.77/0.95 constr_CONST_1: $i)).
% 0.77/0.95 tff(tuple_assoc_pair_type, type, (
% 0.77/0.95 tuple_assoc_pair: ( $i * $i ) > $i)).
% 0.77/0.95 tff(tuple_2_type, type, (
% 0.77/0.95 tuple_2: ( $i * $i ) > $i)).
% 0.77/0.95 tff(name_objective_type, type, (
% 0.77/0.95 name_objective: $i)).
% 0.77/0.95 tff(name_Nb_type, type, (
% 0.77/0.95 name_Nb: $i > $i)).
% 0.77/0.95 tff(tptp_fun_VAR_V_711_0_type, type, (
% 0.77/0.95 tptp_fun_VAR_V_711_0: $i)).
% 0.77/0.95 tff(constr_assoc_pair_2_get_1_type, type, (
% 0.77/0.95 constr_assoc_pair_2_get_1: $i > $i)).
% 0.77/0.95 tff(name_skS_type, type, (
% 0.77/0.95 name_skS: $i)).
% 0.77/0.95 tff(1,plain,
% 0.77/0.95 (^[VAR_X0X30_11: $i, VAR_X1_12: $i] : refl((constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12) <=> (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(2,plain,
% 0.77/0.95 (![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12) <=> ![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1])).
% 0.77/0.95 tff(3,plain,
% 0.77/0.95 (![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12) <=> ![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(4,axiom,(![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax85')).
% 0.77/0.95 tff(5,plain,
% 0.77/0.95 (![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.77/0.95 tff(6,plain,(
% 0.77/0.95 ![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)),
% 0.77/0.95 inference(skolemize,[status(sab)],[5])).
% 0.77/0.96 tff(7,plain,
% 0.77/0.96 (![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.77/0.96 tff(8,plain,
% 0.77/0.96 ((~![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)) | (constr_assoc_pair_2_get_1(tuple_assoc_pair(name_skS, tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)))) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(9,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(name_skS, tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)))) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.77/0.96 tff(10,plain,
% 0.77/0.96 (^[VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : refl((tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30)) <=> (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30)))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(11,plain,
% 0.77/0.96 (![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30)) <=> ![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[10])).
% 0.77/0.96 tff(12,plain,
% 0.77/0.96 (![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30)) <=> ![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(13,axiom,(![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax82')).
% 0.77/0.96 tff(14,plain,
% 0.77/0.96 (![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.77/0.96 tff(15,plain,(
% 0.77/0.96 ![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))),
% 0.77/0.96 inference(skolemize,[status(sab)],[14])).
% 0.77/0.96 tff(16,plain,
% 0.77/0.96 (![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.77/0.96 tff(17,plain,
% 0.77/0.96 ((~![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))) | (tuple_assoc_pair(name_skS, tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective))) = tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(18,plain,
% 0.77/0.96 (tuple_assoc_pair(name_skS, tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective))) = tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.77/0.96 tff(19,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(name_skS, tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[18])).
% 0.77/0.96 tff(20,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(name_skS, tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective))))),
% 0.77/0.96 inference(symmetry,[status(thm)],[19])).
% 0.77/0.96 tff(21,plain,
% 0.77/0.96 ((~![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)) | (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective))) = tuple_2(name_Nb(VAR_V_711!0), name_objective))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(22,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective))) = tuple_2(name_Nb(VAR_V_711!0), name_objective)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[21, 7])).
% 0.77/0.96 tff(23,plain,
% 0.77/0.96 (tuple_2(name_Nb(VAR_V_711!0), name_objective) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(name_skS, tuple_2(name_Nb(VAR_V_711!0), name_objective)), tuple_2(name_Nb(VAR_V_711!0), name_objective)))),
% 0.77/0.96 inference(symmetry,[status(thm)],[22])).
% 0.77/0.96 tff(24,plain,
% 0.77/0.96 (tuple_2(name_Nb(VAR_V_711!0), name_objective) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective))),
% 0.77/0.96 inference(transitivity,[status(thm)],[23, 20, 9])).
% 0.77/0.96 tff(25,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1)),
% 0.77/0.96 inference(monotonicity,[status(thm)],[24])).
% 0.77/0.96 tff(26,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)),
% 0.77/0.96 inference(symmetry,[status(thm)],[25])).
% 0.77/0.96 tff(27,plain,
% 0.77/0.96 ((~![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)) | (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(28,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[27, 7])).
% 0.77/0.96 tff(29,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1)) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[26])).
% 0.77/0.96 tff(30,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1))),
% 0.77/0.96 inference(symmetry,[status(thm)],[29])).
% 0.77/0.96 tff(31,plain,
% 0.77/0.96 ((~![VAR_X_17: $i, VAR_Y_18: $i, VAR_Z_0X30: $i] : (tuple_assoc_pair(VAR_X_17, tuple_assoc_pair(VAR_Y_18, VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17, VAR_Y_18), VAR_Z_0X30))) | (tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(32,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[31, 16])).
% 0.77/0.96 tff(33,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))),
% 0.77/0.96 inference(symmetry,[status(thm)],[32])).
% 0.77/0.96 tff(34,plain,
% 0.77/0.96 (tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1) = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1))),
% 0.77/0.96 inference(transitivity,[status(thm)],[25, 33, 30])).
% 0.77/0.96 tff(35,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_assoc_pair(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), tuple_2(name_Nb(VAR_V_711!0), name_objective)), constr_CONST_1)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[34])).
% 0.77/0.96 tff(36,plain,
% 0.77/0.96 ((~![VAR_X0X30_11: $i, VAR_X1_12: $i] : (constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11, VAR_X1_12)) = VAR_X1_12)) | (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) = constr_CONST_1)),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(37,plain,
% 0.77/0.96 (constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) = constr_CONST_1),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[36, 7])).
% 0.77/0.96 tff(38,plain,
% 0.77/0.96 (constr_CONST_1 = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))),
% 0.77/0.96 inference(symmetry,[status(thm)],[37])).
% 0.77/0.96 tff(39,plain,
% 0.77/0.96 (constr_CONST_1 = tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)),
% 0.77/0.96 inference(transitivity,[status(thm)],[38, 35, 28, 26])).
% 0.77/0.96 tff(40,plain,
% 0.77/0.96 (pred_attacker(constr_CONST_1) <=> pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[39])).
% 0.77/0.96 tff(41,plain,
% 0.77/0.96 (pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)) <=> pred_attacker(constr_CONST_1)),
% 0.77/0.96 inference(symmetry,[status(thm)],[40])).
% 0.77/0.96 tff(42,plain,
% 0.77/0.96 ((~pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))) <=> (~pred_attacker(constr_CONST_1))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[41])).
% 0.77/0.96 tff(43,plain,
% 0.77/0.96 ((~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))) <=> (~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(44,axiom,(~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co0')).
% 0.77/0.96 tff(45,plain,
% 0.77/0.96 (~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.77/0.96 tff(46,plain,
% 0.77/0.96 (~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.77/0.96 tff(47,plain,
% 0.77/0.96 (~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.77/0.96 tff(48,plain,
% 0.77/0.96 (~![VAR_V_711: $i] : pred_attacker(tuple_2(name_Nb(VAR_V_711), name_objective))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.77/0.96 tff(49,plain,(
% 0.77/0.96 ~pred_attacker(tuple_2(name_Nb(VAR_V_711!0), name_objective))),
% 0.77/0.96 inference(skolemize,[status(sab)],[48])).
% 0.77/0.96 tff(50,plain,
% 0.77/0.96 (^[VAR_V_233: $i, VAR_V_234: $i] : refl((pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)))) <=> (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(51,plain,
% 0.77/0.96 (![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)))) <=> ![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[50])).
% 0.77/0.96 tff(52,plain,
% 0.77/0.96 (![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)))) <=> ![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(53,plain,
% 0.77/0.96 (^[VAR_V_233: $i, VAR_V_234: $i] : rewrite((pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)) => pred_attacker(VAR_V_233)) <=> (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(54,plain,
% 0.77/0.96 (![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)) => pred_attacker(VAR_V_233)) <=> ![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[53])).
% 0.77/0.96 tff(55,axiom,(![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234)) => pred_attacker(VAR_V_233))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax143')).
% 0.77/0.96 tff(56,plain,
% 0.77/0.96 (![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.77/0.96 tff(57,plain,
% 0.77/0.96 (![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.77/0.96 tff(58,plain,(
% 0.77/0.96 ![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(skolemize,[status(sab)],[57])).
% 0.77/0.96 tff(59,plain,
% 0.77/0.96 (![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.77/0.96 tff(60,plain,
% 0.77/0.96 (((~![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))) | (pred_attacker(tuple_2(name_Nb(VAR_V_711!0), name_objective)) | (~pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))))) <=> ((~![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))) | pred_attacker(tuple_2(name_Nb(VAR_V_711!0), name_objective)) | (~pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(61,plain,
% 0.77/0.96 ((~![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))) | (pred_attacker(tuple_2(name_Nb(VAR_V_711!0), name_objective)) | (~pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(62,plain,
% 0.77/0.96 ((~![VAR_V_233: $i, VAR_V_234: $i] : (pred_attacker(VAR_V_233) | (~pred_attacker(tuple_assoc_pair(VAR_V_233, VAR_V_234))))) | pred_attacker(tuple_2(name_Nb(VAR_V_711!0), name_objective)) | (~pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.77/0.96 tff(63,plain,
% 0.77/0.96 (~pred_attacker(tuple_assoc_pair(tuple_2(name_Nb(VAR_V_711!0), name_objective), constr_CONST_1))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 0.77/0.96 tff(64,plain,
% 0.77/0.96 (~pred_attacker(constr_CONST_1)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[63, 42])).
% 0.77/0.96 tff(65,plain,
% 0.77/0.96 (pred_attacker(constr_CONST_1) <=> pred_attacker(constr_CONST_1)),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(66,axiom,(pred_attacker(constr_CONST_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax150')).
% 0.77/0.96 tff(67,plain,
% 0.77/0.96 (pred_attacker(constr_CONST_1)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.77/0.96 tff(68,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.77/0.96 % SZS output end Proof
% 0.77/0.96 % E exiting
%------------------------------------------------------------------------------