%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV406+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 : n011.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 05:22:06 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 149 ( 16 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 154 ( 56 ~; 66 |; 14 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 137 ( 17 sgn 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l42_co,conjecture,
! [X1] :
( ! [X2,X3] :
( check_cpq(triple(X2,X1,X3))
<=> ! [X4,X5] :
( pair_in_list(X1,X4,X5)
=> less_than(X5,X4) ) )
=> ! [X6,X7,X8,X9] :
( check_cpq(triple(X6,insert_slb(X1,pair(X8,X9)),X7))
<=> ! [X10,X11] :
( pair_in_list(insert_slb(X1,pair(X8,X9)),X10,X11)
=> less_than(X11,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_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(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(ax38,axiom,
! [X1,X2,X3,X4,X5] :
( strictly_less_than(X4,X5)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax38) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(ax37,axiom,
! [X1,X2,X3,X4,X5] :
( less_than(X5,X4)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> check_cpq(triple(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax37) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ! [X2,X3] :
( check_cpq(triple(X2,X1,X3))
<=> ! [X4,X5] :
( pair_in_list(X1,X4,X5)
=> less_than(X5,X4) ) )
=> ! [X6,X7,X8,X9] :
( check_cpq(triple(X6,insert_slb(X1,pair(X8,X9)),X7))
<=> ! [X10,X11] :
( pair_in_list(insert_slb(X1,pair(X8,X9)),X10,X11)
=> less_than(X11,X10) ) ) ),
inference(assume_negation,[status(cth)],[l42_co]) ).
fof(c_0_7,plain,
! [X159,X160,X161,X162,X163] :
( ( X160 = X161
| pair_in_list(X159,X161,X163)
| ~ pair_in_list(insert_slb(X159,pair(X160,X162)),X161,X163) )
& ( X162 = X163
| pair_in_list(X159,X161,X163)
| ~ pair_in_list(insert_slb(X159,pair(X160,X162)),X161,X163) )
& ( ~ pair_in_list(X159,X161,X163)
| pair_in_list(insert_slb(X159,pair(X160,X162)),X161,X163) )
& ( X160 != X161
| X162 != X163
| pair_in_list(insert_slb(X159,pair(X160,X162)),X161,X163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_8,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
fof(c_0_9,negated_conjecture,
! [X254,X255,X256,X257,X266,X267] :
( ( ~ check_cpq(triple(X254,esk1_0,X255))
| ~ pair_in_list(esk1_0,X256,X257)
| less_than(X257,X256) )
& ( pair_in_list(esk1_0,esk2_2(X254,X255),esk3_2(X254,X255))
| check_cpq(triple(X254,esk1_0,X255)) )
& ( ~ less_than(esk3_2(X254,X255),esk2_2(X254,X255))
| check_cpq(triple(X254,esk1_0,X255)) )
& ( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) )
& ( ~ less_than(esk9_0,esk8_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) )
& ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| ~ pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),X266,X267)
| less_than(X267,X266) ) ),
inference(distribute,[status(thm)],[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_10,plain,
! [X1,X2,X3,X4,X5] :
( strictly_less_than(X4,X5)
=> ~ check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_11,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X146,X147] :
( ( less_than(X146,X147)
| ~ strictly_less_than(X146,X147) )
& ( ~ less_than(X147,X146)
| ~ strictly_less_than(X146,X147) )
& ( ~ less_than(X146,X147)
| less_than(X147,X146)
| strictly_less_than(X146,X147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X143,X144] :
( less_than(X143,X144)
| less_than(X144,X143) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_14,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| less_than(X2,X1)
| ~ pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,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]) ).
fof(c_0_16,plain,
! [X205,X206,X207,X208,X209] :
( ~ strictly_less_than(X208,X209)
| ~ check_cpq(triple(X205,insert_slb(X206,pair(X208,X209)),X207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_17,plain,
pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).
cnf(c_0_18,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X200,X201,X202,X203,X204] :
( ( ~ check_cpq(triple(X200,insert_slb(X201,pair(X203,X204)),X202))
| check_cpq(triple(X200,X201,X202))
| ~ less_than(X204,X203) )
& ( ~ check_cpq(triple(X200,X201,X202))
| check_cpq(triple(X200,insert_slb(X201,pair(X203,X204)),X202))
| ~ less_than(X204,X203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).
cnf(c_0_21,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| less_than(X1,X2)
| ~ pair_in_list(esk1_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( pair_in_list(esk1_0,esk2_2(X1,X2),esk3_2(X1,X2))
| check_cpq(triple(X1,esk1_0,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
( check_cpq(triple(X1,esk1_0,X2))
| ~ less_than(esk3_2(X1,X2),esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( ~ strictly_less_than(X1,X2)
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| less_than(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_26,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( check_cpq(triple(X1,X2,X5))
| ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| check_cpq(triple(X1,esk1_0,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
less_than(esk7_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,plain,
( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
| ~ check_cpq(triple(X1,X2,X3))
| ~ less_than(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( check_cpq(triple(esk4_0,esk1_0,esk5_0))
| check_cpq(triple(X1,esk1_0,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,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_34,negated_conjecture,
( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
( ~ less_than(esk9_0,esk8_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_36,negated_conjecture,
( less_than(X4,X3)
| ~ check_cpq(triple(X1,esk1_0,X2))
| ~ pair_in_list(esk1_0,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_37,negated_conjecture,
check_cpq(triple(esk4_0,esk1_0,esk5_0)),
inference(ef,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( esk8_0 = esk6_0
| pair_in_list(esk1_0,esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( ~ check_cpq(triple(esk4_0,esk1_0,esk5_0))
| ~ less_than(esk9_0,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_29])]) ).
cnf(c_0_40,negated_conjecture,
( check_cpq(triple(X1,esk1_0,X2))
| ~ less_than(esk9_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_41,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_42,negated_conjecture,
( less_than(X1,X2)
| ~ pair_in_list(esk1_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( esk8_0 = esk6_0
| pair_in_list(esk1_0,esk8_0,esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_37])]) ).
cnf(c_0_44,negated_conjecture,
~ less_than(esk9_0,esk8_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( esk9_0 = esk7_0
| pair_in_list(esk1_0,esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_46,negated_conjecture,
esk8_0 = esk6_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( esk9_0 = esk7_0
| pair_in_list(esk1_0,esk6_0,esk9_0) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_37])]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
~ less_than(esk9_0,esk6_0),
inference(rw,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
esk9_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_48]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV406+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 05:06:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------