%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET601+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 May 5 05:08:05 PM UTC 2026
% Result : Theorem 60.64s 35.51s
% Output : CNFRefutation 60.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 154 ( 13 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_intersection,axiom,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection) ).
fof(idempotency_of_intersection,axiom,
! [X1] : intersection(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_intersection) ).
fof(associativity_of_union,axiom,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(union_distributes_over_intersection,axiom,
! [X1,X2,X3] : union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
fof(prove_th72,conjecture,
! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th72) ).
fof(associativity_of_intersection,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(c_0_8,plain,
! [X45,X46] : union(X45,intersection(X45,X46)) = X45,
inference(variable_rename,[status(thm)],[union_intersection]) ).
fof(c_0_9,plain,
! [X41] : intersection(X41,X41) = X41,
inference(variable_rename,[status(thm)],[idempotency_of_intersection]) ).
fof(c_0_10,plain,
! [X38,X39,X40] : union(union(X38,X39),X40) = union(X38,union(X39,X40)),
inference(variable_rename,[status(thm)],[associativity_of_union]) ).
cnf(c_0_11,plain,
union(X1,intersection(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
intersection(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X60,X61] : intersection(X60,X61) = intersection(X61,X60),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_14,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
union(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X58,X59] : union(X58,X59) = union(X59,X58),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_17,plain,
! [X47,X48,X49] : union(X47,intersection(X48,X49)) = intersection(union(X47,X48),union(X47,X49)),
inference(variable_rename,[status(thm)],[union_distributes_over_intersection]) ).
cnf(c_0_18,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
inference(assume_negation,[status(cth)],[prove_th72]) ).
cnf(c_0_20,plain,
union(X1,union(X1,X2)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
union(X1,intersection(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
fof(c_0_24,negated_conjecture,
union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_25,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
intersection(X1,union(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_23]),c_0_18]) ).
cnf(c_0_27,negated_conjecture,
union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
intersection(union(X1,X2),union(X3,X1)) = union(X1,intersection(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_29,plain,
intersection(X1,union(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
fof(c_0_30,plain,
! [X42,X43,X44] : intersection(intersection(X42,X43),X44) = intersection(X42,intersection(X43,X44)),
inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).
cnf(c_0_31,negated_conjecture,
intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk3_0,esk5_0)) != union(intersection(esk5_0,esk3_0),union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_21]),c_0_21]) ).
cnf(c_0_32,plain,
union(X1,intersection(X2,union(X3,X1))) = union(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_28]) ).
cnf(c_0_33,plain,
intersection(X1,union(X2,union(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_14]) ).
cnf(c_0_34,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
intersection(union(esk3_0,esk5_0),intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk5_0),union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_18]),c_0_18]) ).
cnf(c_0_36,plain,
union(X1,union(X2,X3)) = union(X2,union(X3,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_37,plain,
intersection(union(X1,X2),union(X3,X1)) = union(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_38,plain,
intersection(X1,intersection(X2,union(X3,X1))) = intersection(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_11]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
intersection(union(esk3_0,esk5_0),intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_21]) ).
cnf(c_0_40,plain,
intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_41,plain,
intersection(union(X1,X2),union(X3,X2)) = union(X2,intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_42,plain,
intersection(X1,union(X2,intersection(X3,X1))) = intersection(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_43,negated_conjecture,
intersection(union(esk3_0,esk4_0),intersection(union(esk3_0,esk5_0),union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_18]) ).
cnf(c_0_44,plain,
intersection(union(X1,X2),intersection(union(X1,X3),X4)) = intersection(union(X1,intersection(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_45,plain,
union(intersection(X1,X2),intersection(X2,X3)) = intersection(X2,union(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_23]),c_0_42]) ).
cnf(c_0_46,plain,
union(X1,union(intersection(X2,X1),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_47,plain,
intersection(X1,intersection(union(X1,X2),X3)) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_48,plain,
union(X1,union(X2,X3)) = union(X2,union(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_14]) ).
cnf(c_0_49,plain,
union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_50,plain,
intersection(union(X1,X2),union(X2,X3)) = union(X2,intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_51,negated_conjecture,
union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))) != intersection(union(esk4_0,esk5_0),union(esk3_0,intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_18]) ).
cnf(c_0_52,plain,
union(intersection(X1,X2),intersection(X3,X2)) = intersection(X2,union(X3,X1)),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_53,plain,
intersection(union(X1,union(X2,X3)),union(X4,X3)) = union(X3,intersection(union(X1,X2),X4)),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_54,plain,
union(intersection(X1,X2),union(intersection(union(X1,X3),X2),X4)) = union(intersection(union(X1,X3),X2),X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
union(X1,intersection(X2,intersection(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_56,plain,
union(X1,union(X2,intersection(X1,X3))) = union(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_57,plain,
intersection(union(X1,X2),union(X3,union(X4,X2))) = union(X2,intersection(X1,union(X3,X4))),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_58,negated_conjecture,
intersection(union(esk4_0,esk5_0),union(esk3_0,intersection(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),intersection(esk5_0,union(esk3_0,esk4_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_21]) ).
cnf(c_0_59,plain,
intersection(union(X1,X2),union(X3,intersection(X4,X2))) = union(intersection(X4,X2),intersection(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_53,c_0_23]) ).
cnf(c_0_60,plain,
intersection(X1,union(X2,X3)) = intersection(union(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_52]),c_0_14]),c_0_25]) ).
cnf(c_0_61,plain,
intersection(union(X1,X2),union(X3,intersection(X1,X4))) = union(intersection(X1,X4),intersection(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_62,plain,
intersection(union(X1,intersection(X2,X3)),union(X4,X3)) = union(intersection(X2,X3),intersection(X1,union(X4,X3))),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
cnf(c_0_63,negated_conjecture,
union(intersection(esk4_0,esk5_0),intersection(esk3_0,union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),intersection(esk5_0,union(esk3_0,esk4_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_21]) ).
cnf(c_0_64,plain,
union(intersection(X1,X2),intersection(union(X1,X3),X4)) = union(intersection(X3,X4),intersection(X1,union(X2,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_41]),c_0_61]),c_0_62]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_60]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET601+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:27:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 60.64/35.51 % Version : CSE_E---1.7
% 60.64/35.51 % Problem : theBenchmark.p
% 60.64/35.51 % SZS status Theorem for theBenchmark.p
% 60.64/35.51 % SZS output start CNFRefutation
% See solution above
% 60.84/35.76 % Total time : 26.432s
%------------------------------------------------------------------------------