%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET351+4 : 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 : n014.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 05:07:46 PM UTC 2026
% Result : Theorem 5.45s 4.37s
% Output : CNFRefutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 94 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 97 ( 42 ~; 39 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI39,conjecture,
! [X1] : equal_set(sum(singleton(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] : equal_set(sum(singleton(X1)),X1),
inference(assume_negation,[status(cth)],[thI39]) ).
fof(c_0_7,negated_conjecture,
~ equal_set(sum(singleton(esk4_0)),esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X41,X42] :
( ( subset(X41,X42)
| ~ equal_set(X41,X42) )
& ( subset(X42,X41)
| ~ equal_set(X41,X42) )
& ( ~ subset(X41,X42)
| ~ subset(X42,X41)
| equal_set(X41,X42) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_9,negated_conjecture,
~ equal_set(sum(singleton(esk4_0)),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X43,X44] :
( ( ~ member(X43,power_set(X44))
| subset(X43,X44) )
& ( ~ subset(X43,X44)
| member(X43,power_set(X44)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
cnf(c_0_12,negated_conjecture,
( ~ subset(esk4_0,sum(singleton(esk4_0)))
| ~ subset(sum(singleton(esk4_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X35,X36,X37,X38,X39] :
( ( ~ subset(X35,X36)
| ~ member(X37,X35)
| member(X37,X36) )
& ( member(esk1_2(X38,X39),X38)
| subset(X38,X39) )
& ( ~ member(esk1_2(X38,X39),X39)
| subset(X38,X39) ) ),
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])])])])])]) ).
fof(c_0_15,plain,
! [X60,X61,X63,X64,X65] :
( ( member(esk2_2(X60,X61),X61)
| ~ member(X60,sum(X61)) )
& ( member(X60,esk2_2(X60,X61))
| ~ member(X60,sum(X61)) )
& ( ~ member(X65,X64)
| ~ member(X63,X65)
| member(X63,sum(X64)) ) ),
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)],[sum])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(sum(singleton(esk4_0)),power_set(esk4_0))
| ~ subset(esk4_0,sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X55,X56] :
( ( ~ member(X55,singleton(X56))
| X55 = X56 )
& ( X55 != X56
| member(X55,singleton(X56)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0)
| ~ member(sum(singleton(esk4_0)),power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0)))
| ~ member(sum(singleton(esk4_0)),power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(X1))
| ~ member(sum(singleton(esk4_0)),power_set(esk4_0))
| ~ member(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( esk2_2(X1,singleton(X2)) = X2
| ~ member(X1,sum(singleton(X2))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( member(esk1_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
~ member(sum(singleton(esk4_0)),power_set(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,plain,
( esk2_2(esk1_2(sum(singleton(X1)),X2),singleton(X1)) = X1
| member(sum(singleton(X1)),power_set(X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0)
| ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,plain,
( member(X1,power_set(X2))
| ~ member(esk1_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_37,negated_conjecture,
member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_31]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET351+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 02:20:51 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 5.45/4.37 % Version : CSE_E---1.7
% 5.45/4.37 % Problem : theBenchmark.p
% 5.45/4.37 % SZS status Theorem for theBenchmark.p
% 5.45/4.37 % SZS output start CNFRefutation
% See solution above
% 5.45/4.39 % Total time : 3.371s
%------------------------------------------------------------------------------