TSTP Solution File: SET559-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET559-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Tue Sep 20 05:07:02 EDT 2022
% Result : Unsatisfiable 142.74s 92.06s
% Output : Proof 142.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET559-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 07:03:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 142.74/92.06 % SZS status Unsatisfiable
% 142.74/92.06 % SZS output start Proof
% 142.74/92.06 tff(member_type, type, (
% 142.74/92.06 member: ( $i * $i ) > $o)).
% 142.74/92.06 tff(domain_of_type, type, (
% 142.74/92.06 domain_of: $i > $i)).
% 142.74/92.06 tff(xf2_type, type, (
% 142.74/92.06 xf2: $i)).
% 142.74/92.06 tff(second_type, type, (
% 142.74/92.06 second: $i > $i)).
% 142.74/92.06 tff(not_subclass_element_type, type, (
% 142.74/92.06 not_subclass_element: ( $i * $i ) > $i)).
% 142.74/92.06 tff(cross_product_type, type, (
% 142.74/92.06 cross_product: ( $i * $i ) > $i)).
% 142.74/92.06 tff(range_of_type, type, (
% 142.74/92.06 range_of: $i > $i)).
% 142.74/92.06 tff(xh_type, type, (
% 142.74/92.06 xh: $i)).
% 142.74/92.06 tff(first_type, type, (
% 142.74/92.06 first: $i > $i)).
% 142.74/92.06 tff(ordered_pair_type, type, (
% 142.74/92.06 ordered_pair: ( $i * $i ) > $i)).
% 142.74/92.06 tff(subclass_type, type, (
% 142.74/92.06 subclass: ( $i * $i ) > $o)).
% 142.74/92.06 tff(compatible_type, type, (
% 142.74/92.06 compatible: ( $i * $i * $i ) > $o)).
% 142.74/92.06 tff(xf1_type, type, (
% 142.74/92.06 xf1: $i)).
% 142.74/92.06 tff(operation_type, type, (
% 142.74/92.06 operation: $i > $o)).
% 142.74/92.06 tff(1,assumption,(~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))), introduced(assumption)).
% 142.74/92.06 tff(2,plain,
% 142.74/92.06 ((~subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))) <=> (~subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))),
% 142.74/92.06 inference(rewrite,[status(thm)],[])).
% 142.74/92.06 tff(3,axiom,(~subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_compatible_functions_alternate_defn2_3')).
% 142.74/92.06 tff(4,plain,
% 142.74/92.06 (~subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))),
% 142.74/92.06 inference(modus_ponens,[status(thm)],[3, 2])).
% 142.74/92.06 tff(5,plain,
% 142.74/92.06 (^[Y: $i, X: $i] : refl((subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> (subclass(X, Y) | member(not_subclass_element(X, Y), X)))),
% 142.74/92.06 inference(bind,[status(th)],[])).
% 142.74/92.06 tff(6,plain,
% 142.74/92.06 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(quant_intro,[status(thm)],[5])).
% 142.74/92.06 tff(7,plain,
% 142.74/92.06 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(rewrite,[status(thm)],[])).
% 142.74/92.06 tff(8,plain,
% 142.74/92.06 (^[Y: $i, X: $i] : rewrite((member(not_subclass_element(X, Y), X) | subclass(X, Y)) <=> (subclass(X, Y) | member(not_subclass_element(X, Y), X)))),
% 142.74/92.06 inference(bind,[status(th)],[])).
% 142.74/92.06 tff(9,plain,
% 142.74/92.06 (![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(quant_intro,[status(thm)],[8])).
% 142.74/92.06 tff(10,axiom,(![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','not_subclass_members1')).
% 142.74/92.06 tff(11,plain,
% 142.74/92.06 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(modus_ponens,[status(thm)],[10, 9])).
% 142.74/92.06 tff(12,plain,
% 142.74/92.06 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(modus_ponens,[status(thm)],[11, 7])).
% 142.74/92.06 tff(13,plain,(
% 142.74/92.06 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(skolemize,[status(sab)],[12])).
% 142.74/92.06 tff(14,plain,
% 142.74/92.06 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 142.74/92.06 inference(modus_ponens,[status(thm)],[13, 6])).
% 142.74/92.06 tff(15,plain,
% 142.74/92.06 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)) | member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh))))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)) | member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh))))),
% 142.74/92.06 inference(rewrite,[status(thm)],[])).
% 142.74/92.06 tff(16,plain,
% 142.74/92.06 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)) | member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh))))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(17,plain,
% 142.74/92.07 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)) | member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[16, 15])).
% 142.74/92.07 tff(18,plain,
% 142.74/92.07 (member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[17, 14, 4])).
% 142.74/92.07 tff(19,plain,
% 142.74/92.07 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(20,plain,
% 142.74/92.07 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[19])).
% 142.74/92.07 tff(21,plain,
% 142.74/92.07 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(22,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product4')).
% 142.74/92.07 tff(23,plain,
% 142.74/92.07 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[22, 21])).
% 142.74/92.07 tff(24,plain,(
% 142.74/92.07 ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 142.74/92.07 inference(skolemize,[status(sab)],[23])).
% 142.74/92.07 tff(25,plain,
% 142.74/92.07 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[24, 20])).
% 142.74/92.07 tff(26,plain,
% 142.74/92.07 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))) | (ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))) = not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))) | (ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))) = not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(27,plain,
% 142.74/92.07 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))) | (ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))) = not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(28,plain,
% 142.74/92.07 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))) | (ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))) = not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[27, 26])).
% 142.74/92.07 tff(29,plain,
% 142.74/92.07 (ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))) = not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[28, 25, 18])).
% 142.74/92.07 tff(30,plain,
% 142.74/92.07 (member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh))) <=> member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh)))),
% 142.74/92.07 inference(monotonicity,[status(thm)],[29])).
% 142.74/92.07 tff(31,plain,
% 142.74/92.07 (member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), cross_product(range_of(xh), range_of(xh))) <=> member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))),
% 142.74/92.07 inference(symmetry,[status(thm)],[30])).
% 142.74/92.07 tff(32,plain,
% 142.74/92.07 (member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[18, 31])).
% 142.74/92.07 tff(33,plain,
% 142.74/92.07 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(34,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[33])).
% 142.74/92.07 tff(35,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(36,axiom,(![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product1')).
% 142.74/92.07 tff(37,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[36, 35])).
% 142.74/92.07 tff(38,plain,(
% 142.74/92.07 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 142.74/92.07 inference(skolemize,[status(sab)],[37])).
% 142.74/92.07 tff(39,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[38, 34])).
% 142.74/92.07 tff(40,plain,
% 142.74/92.07 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | ((~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | (~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(41,plain,
% 142.74/92.07 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | ((~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(42,plain,
% 142.74/92.07 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | (~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[41, 40])).
% 142.74/92.07 tff(43,plain,
% 142.74/92.07 ((~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[42, 39])).
% 142.74/92.07 tff(44,plain,
% 142.74/92.07 (member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[43, 32])).
% 142.74/92.07 tff(45,plain,
% 142.74/92.07 (compatible(xh, xf1, xf2) <=> compatible(xh, xf1, xf2)),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(46,axiom,(compatible(xh, xf1, xf2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_compatible_functions_alternate_defn2_2')).
% 142.74/92.07 tff(47,plain,
% 142.74/92.07 (compatible(xh, xf1, xf2)),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[46, 45])).
% 142.74/92.07 tff(48,plain,
% 142.74/92.07 (^[Xf2: $i, Xf1: $i, Xh: $i] : refl(((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2)))) <=> ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2)))))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(49,plain,
% 142.74/92.07 (![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2)))) <=> ![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[48])).
% 142.74/92.07 tff(50,plain,
% 142.74/92.07 (![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2)))) <=> ![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(51,axiom,(![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','compatible3')).
% 142.74/92.07 tff(52,plain,
% 142.74/92.07 (![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[51, 50])).
% 142.74/92.07 tff(53,plain,(
% 142.74/92.07 ![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))),
% 142.74/92.07 inference(skolemize,[status(sab)],[52])).
% 142.74/92.07 tff(54,plain,
% 142.74/92.07 (![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[53, 49])).
% 142.74/92.07 tff(55,plain,
% 142.74/92.07 (((~![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))) | ((~compatible(xh, xf1, xf2)) | subclass(range_of(xh), domain_of(domain_of(xf2))))) <=> ((~![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))) | (~compatible(xh, xf1, xf2)) | subclass(range_of(xh), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(56,plain,
% 142.74/92.07 ((~![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))) | ((~compatible(xh, xf1, xf2)) | subclass(range_of(xh), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(57,plain,
% 142.74/92.07 ((~![Xf2: $i, Xf1: $i, Xh: $i] : ((~compatible(Xh, Xf1, Xf2)) | subclass(range_of(Xh), domain_of(domain_of(Xf2))))) | (~compatible(xh, xf1, xf2)) | subclass(range_of(xh), domain_of(domain_of(xf2)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[56, 55])).
% 142.74/92.07 tff(58,plain,
% 142.74/92.07 (subclass(range_of(xh), domain_of(domain_of(xf2)))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 142.74/92.07 tff(59,plain,
% 142.74/92.07 (^[Y: $i, U: $i, X: $i] : refl((member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(60,plain,
% 142.74/92.07 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[59])).
% 142.74/92.07 tff(61,plain,
% 142.74/92.07 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(62,plain,
% 142.74/92.07 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | (~member(U, X))) <=> ((~member(U, X)) | (~subclass(X, Y)))), ((((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (((~member(U, X)) | (~subclass(X, Y))) | member(U, Y)))), rewrite((((~member(U, X)) | (~subclass(X, Y))) | member(U, Y)) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))), ((((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(63,plain,
% 142.74/92.07 (![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[62])).
% 142.74/92.07 tff(64,axiom,(![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','subclass_members')).
% 142.74/92.07 tff(65,plain,
% 142.74/92.07 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[64, 63])).
% 142.74/92.07 tff(66,plain,
% 142.74/92.07 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[65, 61])).
% 142.74/92.07 tff(67,plain,(
% 142.74/92.07 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(skolemize,[status(sab)],[66])).
% 142.74/92.07 tff(68,plain,
% 142.74/92.07 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[67, 60])).
% 142.74/92.07 tff(69,plain,
% 142.74/92.07 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(70,plain,
% 142.74/92.07 ((member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2))))) <=> ((~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(71,plain,
% 142.74/92.07 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))))),
% 142.74/92.07 inference(monotonicity,[status(thm)],[70])).
% 142.74/92.07 tff(72,plain,
% 142.74/92.07 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))),
% 142.74/92.07 inference(transitivity,[status(thm)],[71, 69])).
% 142.74/92.07 tff(73,plain,
% 142.74/92.07 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(74,plain,
% 142.74/92.07 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[73, 72])).
% 142.74/92.07 tff(75,plain,
% 142.74/92.07 ($false),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[74, 68, 58, 44, 1])).
% 142.74/92.07 tff(76,plain,(member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))), inference(lemma,lemma(discharge,[]))).
% 142.74/92.07 tff(77,plain,
% 142.74/92.07 (operation(xf2) <=> operation(xf2)),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(78,axiom,(operation(xf2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_compatible_functions_alternate_defn2_1')).
% 142.74/92.07 tff(79,plain,
% 142.74/92.07 (operation(xf2)),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[78, 77])).
% 142.74/92.07 tff(80,plain,
% 142.74/92.07 (^[Xf: $i] : refl(((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf))) <=> ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf))))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(81,plain,
% 142.74/92.07 (![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf))) <=> ![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[80])).
% 142.74/92.07 tff(82,plain,
% 142.74/92.07 (![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf))) <=> ![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(83,axiom,(![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','operation2')).
% 142.74/92.07 tff(84,plain,
% 142.74/92.07 (![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[83, 82])).
% 142.74/92.07 tff(85,plain,(
% 142.74/92.07 ![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))),
% 142.74/92.07 inference(skolemize,[status(sab)],[84])).
% 142.74/92.07 tff(86,plain,
% 142.74/92.07 (![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[85, 81])).
% 142.74/92.07 tff(87,plain,
% 142.74/92.07 (((~![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))) | ((~operation(xf2)) | (cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))) = domain_of(xf2)))) <=> ((~![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))) | (~operation(xf2)) | (cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))) = domain_of(xf2)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(88,plain,
% 142.74/92.07 ((~![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))) | ((~operation(xf2)) | (cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))) = domain_of(xf2)))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(89,plain,
% 142.74/92.07 ((~![Xf: $i] : ((~operation(Xf)) | (cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)))) | (~operation(xf2)) | (cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))) = domain_of(xf2))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[88, 87])).
% 142.74/92.07 tff(90,plain,
% 142.74/92.07 (cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))) = domain_of(xf2)),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[89, 86, 79])).
% 142.74/92.07 tff(91,plain,
% 142.74/92.07 (member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))) <=> member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))),
% 142.74/92.07 inference(monotonicity,[status(thm)],[29, 90])).
% 142.74/92.07 tff(92,plain,
% 142.74/92.07 (member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2)) <=> member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(symmetry,[status(thm)],[91])).
% 142.74/92.07 tff(93,plain,
% 142.74/92.07 ((~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))) <=> (~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))))),
% 142.74/92.07 inference(monotonicity,[status(thm)],[92])).
% 142.74/92.07 tff(94,plain,
% 142.74/92.07 (^[Y: $i, X: $i] : refl(((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(95,plain,
% 142.74/92.07 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[94])).
% 142.74/92.07 tff(96,plain,
% 142.74/92.07 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(97,axiom,(![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','not_subclass_members2')).
% 142.74/92.07 tff(98,plain,
% 142.74/92.07 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[97, 96])).
% 142.74/92.07 tff(99,plain,(
% 142.74/92.07 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 142.74/92.07 inference(skolemize,[status(sab)],[98])).
% 142.74/92.07 tff(100,plain,
% 142.74/92.07 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[99, 95])).
% 142.74/92.07 tff(101,plain,
% 142.74/92.07 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))) | subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))) | subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(102,plain,
% 142.74/92.07 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))) | subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(103,plain,
% 142.74/92.07 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))) | subclass(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[102, 101])).
% 142.74/92.07 tff(104,plain,
% 142.74/92.07 (~member(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)), domain_of(xf2))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[103, 100, 4])).
% 142.74/92.07 tff(105,plain,
% 142.74/92.07 (~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[104, 93])).
% 142.74/92.07 tff(106,plain,
% 142.74/92.07 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(107,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[106])).
% 142.74/92.07 tff(108,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(109,plain,
% 142.74/92.07 (^[V: $i, Y: $i, U: $i, X: $i] : rewrite((((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y))) <=> ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(110,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : (((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[109])).
% 142.74/92.07 tff(111,axiom,(![V: $i, Y: $i, U: $i, X: $i] : (((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product3')).
% 142.74/92.07 tff(112,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[111, 110])).
% 142.74/92.07 tff(113,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[112, 108])).
% 142.74/92.07 tff(114,plain,(
% 142.74/92.07 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(skolemize,[status(sab)],[113])).
% 142.74/92.07 tff(115,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[114, 107])).
% 142.74/92.07 tff(116,plain,
% 142.74/92.07 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))) | member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))) | member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(117,plain,
% 142.74/92.07 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))) | member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))))),
% 142.74/92.07 inference(quant_inst,[status(thm)],[])).
% 142.74/92.07 tff(118,plain,
% 142.74/92.07 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))) | member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[117, 116])).
% 142.74/92.07 tff(119,plain,
% 142.74/92.07 ((~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))) | member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(domain_of(domain_of(xf2)), domain_of(domain_of(xf2)))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[118, 115])).
% 142.74/92.07 tff(120,plain,
% 142.74/92.07 ((~member(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[119, 105])).
% 142.74/92.07 tff(121,plain,
% 142.74/92.07 (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2)))),
% 142.74/92.07 inference(unit_resolution,[status(thm)],[120, 76])).
% 142.74/92.07 tff(122,plain,
% 142.74/92.07 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)) <=> ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)))),
% 142.74/92.07 inference(bind,[status(th)],[])).
% 142.74/92.07 tff(123,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 142.74/92.07 inference(quant_intro,[status(thm)],[122])).
% 142.74/92.07 tff(124,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(125,axiom,(![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product2')).
% 142.74/92.07 tff(126,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[125, 124])).
% 142.74/92.07 tff(127,plain,(
% 142.74/92.07 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 142.74/92.07 inference(skolemize,[status(sab)],[126])).
% 142.74/92.07 tff(128,plain,
% 142.74/92.07 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 142.74/92.07 inference(modus_ponens,[status(thm)],[127, 123])).
% 142.74/92.07 tff(129,plain,
% 142.74/92.07 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | ((~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | (~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))),
% 142.74/92.07 inference(rewrite,[status(thm)],[])).
% 142.74/92.07 tff(130,plain,
% 142.74/92.07 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | ((~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))),
% 142.74/92.08 inference(quant_inst,[status(thm)],[])).
% 142.74/92.08 tff(131,plain,
% 142.74/92.08 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | (~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))),
% 142.74/92.08 inference(modus_ponens,[status(thm)],[130, 129])).
% 142.74/92.08 tff(132,plain,
% 142.74/92.08 ((~member(ordered_pair(first(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2)))), cross_product(range_of(xh), range_of(xh)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))),
% 142.74/92.08 inference(unit_resolution,[status(thm)],[131, 128])).
% 142.74/92.08 tff(133,plain,
% 142.74/92.08 (member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))),
% 142.74/92.08 inference(unit_resolution,[status(thm)],[132, 32])).
% 142.74/92.08 tff(134,plain,
% 142.74/92.08 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))),
% 142.74/92.08 inference(rewrite,[status(thm)],[])).
% 142.74/92.08 tff(135,plain,
% 142.74/92.08 ((member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2))))) <=> ((~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))),
% 142.74/92.08 inference(rewrite,[status(thm)],[])).
% 142.74/92.08 tff(136,plain,
% 142.74/92.08 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))))),
% 142.74/92.08 inference(monotonicity,[status(thm)],[135])).
% 142.74/92.08 tff(137,plain,
% 142.74/92.08 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))))),
% 142.74/92.08 inference(transitivity,[status(thm)],[136, 134])).
% 142.74/92.08 tff(138,plain,
% 142.74/92.08 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))))),
% 142.74/92.08 inference(quant_inst,[status(thm)],[])).
% 142.74/92.08 tff(139,plain,
% 142.74/92.08 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~subclass(range_of(xh), domain_of(domain_of(xf2)))) | member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), domain_of(domain_of(xf2))) | (~member(second(not_subclass_element(cross_product(range_of(xh), range_of(xh)), domain_of(xf2))), range_of(xh)))),
% 142.74/92.08 inference(modus_ponens,[status(thm)],[138, 137])).
% 142.74/92.08 tff(140,plain,
% 142.74/92.08 ($false),
% 142.74/92.08 inference(unit_resolution,[status(thm)],[139, 68, 58, 133, 121])).
% 142.74/92.08 % SZS output end Proof
%------------------------------------------------------------------------------