%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET185+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 : n008.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 05:07:32 PM UTC 2026
% Result : Theorem 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 70 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 23 ~; 28 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_union,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).
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(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,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[prove_subset_union]) ).
fof(c_0_6,plain,
! [X23,X24,X25,X26,X27] :
( ( ~ subset(X23,X24)
| ~ member(X25,X23)
| member(X25,X24) )
& ( member(esk1_2(X26,X27),X26)
| subset(X26,X27) )
& ( ~ member(esk1_2(X26,X27),X27)
| subset(X26,X27) ) ),
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_7,negated_conjecture,
( subset(esk3_0,esk4_0)
& union(esk3_0,esk4_0) != esk4_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X20,X21,X22] :
( ( ~ member(X22,union(X20,X21))
| member(X22,X20)
| member(X22,X21) )
& ( ~ member(X22,X20)
| member(X22,union(X20,X21)) )
& ( ~ member(X22,X21)
| member(X22,union(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,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_13,c_0_14]) ).
fof(c_0_17,plain,
! [X31,X32] : union(X31,X32) = union(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_18,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_19,plain,
! [X29,X30] :
( ( subset(X29,X30)
| X29 != X30 )
& ( subset(X30,X29)
| X29 != X30 )
& ( ~ subset(X29,X30)
| ~ subset(X30,X29)
| X29 = X30 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_20,negated_conjecture,
( subset(union(X1,esk3_0),esk4_0)
| member(esk1_2(union(X1,esk3_0),esk4_0),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(union(esk3_0,esk4_0),esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
union(esk3_0,esk4_0) != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET185+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 : n008.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 02:14:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------