%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV403+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n007.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 05:22:05 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 116 ( 25 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 114 ( 42 ~; 46 |; 15 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 99 ( 6 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l39_co,conjecture,
! [X1] :
( ! [X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) )
=> ! [X5,X6,X7,X8,X9] :
( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& strictly_less_than(X6,X7) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_co) ).
fof(ax23,axiom,
! [X1,X2,X3,X4,X5] :
( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
<=> ( pair_in_list(X1,X3,X5)
| ( X2 = X3
& X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(ax29,axiom,
! [X1,X2,X3,X4] :
( strictly_less_than(X4,X3)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax29) ).
fof(ax30,axiom,
! [X1,X2,X3,X4] :
( less_than(X3,X4)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax30) ).
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ! [X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) )
=> ! [X5,X6,X7,X8,X9] :
( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& strictly_less_than(X6,X7) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
inference(assume_negation,[status(cth)],[l39_co]) ).
fof(c_0_7,plain,
! [X85,X86,X87,X88,X89] :
( ( X86 = X87
| pair_in_list(X85,X87,X89)
| ~ pair_in_list(insert_slb(X85,pair(X86,X88)),X87,X89) )
& ( X88 = X89
| pair_in_list(X85,X87,X89)
| ~ pair_in_list(insert_slb(X85,pair(X86,X88)),X87,X89) )
& ( ~ pair_in_list(X85,X87,X89)
| pair_in_list(insert_slb(X85,pair(X86,X88)),X87,X89) )
& ( X86 != X87
| X88 != X89
| pair_in_list(insert_slb(X85,pair(X86,X88)),X87,X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_8,negated_conjecture,
! [X114,X115,X116] :
( ( ~ pair_in_list(esk1_0,X114,X115)
| ~ strictly_less_than(X115,X116)
| pair_in_list(update_slb(esk1_0,X116),X114,X116) )
& pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
& strictly_less_than(esk3_0,esk4_0)
& ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X105,X106,X107,X108] :
( ~ strictly_less_than(X108,X107)
| update_slb(insert_slb(X105,pair(X106,X108)),X107) = insert_slb(update_slb(X105,X107),pair(X106,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])]) ).
cnf(c_0_10,plain,
( X1 = X2
| pair_in_list(X3,X4,X2)
| ~ pair_in_list(insert_slb(X3,pair(X5,X1)),X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X109,X110,X111,X112] :
( ~ less_than(X111,X112)
| update_slb(insert_slb(X109,pair(X110,X112)),X111) = insert_slb(update_slb(X109,X111),pair(X110,X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])]) ).
cnf(c_0_13,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( update_slb(insert_slb(X3,pair(X4,X1)),X2) = insert_slb(update_slb(X3,X2),pair(X4,X2))
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X3),X1,X3)
| ~ pair_in_list(esk1_0,X1,X2)
| ~ strictly_less_than(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
( esk6_0 = esk3_0
| pair_in_list(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_17,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_0_18,plain,
( update_slb(insert_slb(X3,pair(X4,X2)),X1) = insert_slb(update_slb(X3,X1),pair(X4,X2))
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk4_0)
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( pair_in_list(insert_slb(X1,pair(X4,X5)),X2,X3)
| ~ pair_in_list(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
( esk6_0 = esk3_0
| pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| ~ strictly_less_than(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
strictly_less_than(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_23,plain,
! [X72,X73] :
( ( less_than(X72,X73)
| ~ strictly_less_than(X72,X73) )
& ( ~ less_than(X73,X72)
| ~ strictly_less_than(X72,X73) )
& ( ~ less_than(X72,X73)
| less_than(X73,X72)
| strictly_less_than(X72,X73) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_24,plain,
! [X69,X70] :
( less_than(X69,X70)
| less_than(X70,X69) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_25,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk6_0)),esk2_0,esk4_0)
| ~ less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0)
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( esk6_0 = esk3_0
| pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0)
| ~ less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_31,plain,
( X1 = X2
| pair_in_list(X3,X2,X4)
| ~ pair_in_list(insert_slb(X3,pair(X1,X5)),X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,negated_conjecture,
( esk6_0 = esk3_0
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( esk6_0 = esk3_0
| ~ less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( esk2_0 = esk5_0
| pair_in_list(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_11]) ).
cnf(c_0_36,negated_conjecture,
esk6_0 = esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( esk2_0 = esk5_0
| pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| ~ strictly_less_than(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_36]),c_0_22])]) ).
cnf(c_0_39,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_36]),c_0_22])]) ).
cnf(c_0_41,negated_conjecture,
esk2_0 = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_38]) ).
cnf(c_0_42,plain,
pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_39])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV403+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.16/0.33 % Computer : n007.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 05:06:24 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------