%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET159+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 05:07:28 PM UTC 2026
% Result : Theorem 44.23s 26.30s
% Output : CNFRefutation 44.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 80 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 73 ( 29 ~; 33 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 4 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(prove_associativity_of_union,conjecture,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_union) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_5,plain,
! [X28,X29,X30,X31,X32] :
( ( ~ subset(X28,X29)
| ~ member(X30,X28)
| member(X30,X29) )
& ( member(esk1_2(X31,X32),X31)
| subset(X31,X32) )
& ( ~ member(esk1_2(X31,X32),X32)
| subset(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])]) ).
fof(c_0_6,plain,
! [X21,X22,X23] :
( ( ~ member(X23,union(X21,X22))
| member(X23,X21)
| member(X23,X22) )
& ( ~ member(X23,X21)
| member(X23,union(X21,X22)) )
& ( ~ member(X23,X22)
| member(X23,union(X21,X22)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_14,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_16,plain,
( subset(union(X1,X2),union(X2,X3))
| member(esk1_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
subset(union(X1,X2),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_union]) ).
cnf(c_0_20,plain,
( member(X1,union(X2,union(X3,X4)))
| ~ member(X1,union(X3,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
fof(c_0_22,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_23,plain,
! [X26,X27] : union(X26,X27) = union(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_24,plain,
! [X24,X25] :
( ( subset(X24,X25)
| X24 != X25 )
& ( subset(X25,X24)
| X24 != X25 )
& ( ~ subset(X24,X25)
| ~ subset(X25,X24)
| X24 = X25 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_25,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),union(X3,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_20]) ).
cnf(c_0_26,plain,
( subset(union(X1,X2),union(X3,union(X4,X1)))
| member(esk1_2(union(X1,X2),union(X3,union(X4,X1))),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_27,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
subset(union(X1,union(X2,X3)),union(X3,union(X2,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
union(X1,union(X2,X3)) = union(X3,union(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
union(esk4_0,union(esk3_0,esk5_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
union(X1,union(X2,X3)) = union(X3,union(X1,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET159+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:13:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 44.23/26.30 % Version : CSE_E---1.7
% 44.23/26.30 % Problem : theBenchmark.p
% 44.23/26.30 % SZS status Theorem for theBenchmark.p
% 44.23/26.30 % SZS output start CNFRefutation
% See solution above
% 44.33/26.48 % Total time : 19.404s
%------------------------------------------------------------------------------