%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV394+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 : n018.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 05:22:04 PM UTC 2026
% Result : Theorem 1.38s 1.75s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 115 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 118 ( 47 ~; 42 |; 15 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 121 ( 12 sgn 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(l30_co,conjecture,
! [X1,X2,X3,X4] :
( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
& ok(remove_cpq(triple(X1,X2,X3),X4)) )
=> ! [X5] :
( pair_in_list(X2,X4,X5)
=> less_than(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_co) ).
fof(ax43,axiom,
! [X1,X2,X3,X4] :
( ~ contains_slb(X2,X4)
=> remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax43) ).
fof(ax45,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,lookup_slb(X2,X4)) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax45) ).
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(l30_li4142,lemma,
! [X1,X2,X3] :
( check_cpq(triple(X1,X2,X3))
<=> ! [X4,X5] :
( pair_in_list(X2,X4,X5)
=> less_than(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_li4142) ).
fof(ax44,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& less_than(lookup_slb(X2,X4),X4) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax44) ).
fof(l30_li3132,lemma,
! [X1,X2,X3,X4,X5] :
( ( pair_in_list(X2,X4,X5)
& strictly_less_than(X4,X5)
& ok(remove_cpq(triple(X1,X2,X3),X4)) )
=> pair_in_list(remove_slb(X2,X4),X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_li3132) ).
fof(c_0_9,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
& ok(remove_cpq(triple(X1,X2,X3),X4)) )
=> ! [X5] :
( pair_in_list(X2,X4,X5)
=> less_than(X5,X4) ) ),
inference(assume_negation,[status(cth)],[l30_co]) ).
fof(c_0_11,plain,
! [X1,X2,X3,X4] :
( ~ contains_slb(X2,X4)
=> remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
inference(fof_simplification,[status(thm)],[ax43]) ).
fof(c_0_12,plain,
! [X212,X213] : ~ ok(triple(X212,X213,bad)),
inference(variable_rename,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X229,X230,X231,X232] :
( ~ contains_slb(X230,X232)
| ~ strictly_less_than(X232,lookup_slb(X230,X232))
| remove_cpq(triple(X229,X230,X231),X232) = triple(remove_pqp(X229,X232),remove_slb(X230,X232),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(c_0_14,negated_conjecture,
( check_cpq(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0))
& ok(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0))
& pair_in_list(esk4_0,esk6_0,esk7_0)
& ~ less_than(esk7_0,esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_15,plain,
! [X221,X222,X223,X224] :
( contains_slb(X222,X224)
| remove_cpq(triple(X221,X222,X223),X224) = triple(X221,X222,bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_16,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_17,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),bad)
| ~ contains_slb(X1,X2)
| ~ strictly_less_than(X2,lookup_slb(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
ok(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( contains_slb(X1,X2)
| remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X144,X145] :
( ( less_than(X144,X145)
| ~ strictly_less_than(X144,X145) )
& ( ~ less_than(X145,X144)
| ~ strictly_less_than(X144,X145) )
& ( ~ less_than(X144,X145)
| less_than(X145,X144)
| strictly_less_than(X144,X145) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_22,plain,
! [X141,X142] :
( less_than(X141,X142)
| less_than(X142,X141) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(c_0_23,lemma,
! [X251,X252,X253,X254,X255,X256,X257,X260] :
( ( ~ check_cpq(triple(X251,X252,X253))
| ~ pair_in_list(X252,X254,X255)
| less_than(X255,X254) )
& ( pair_in_list(X257,esk1_2(X256,X257),esk2_2(X256,X257))
| check_cpq(triple(X256,X257,X260)) )
& ( ~ less_than(esk2_2(X256,X257),esk1_2(X256,X257))
| check_cpq(triple(X256,X257,X260)) ) ),
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)],[l30_li4142])])])])])]) ).
fof(c_0_24,plain,
! [X225,X226,X227,X228] :
( ~ contains_slb(X226,X228)
| ~ less_than(lookup_slb(X226,X228),X228)
| remove_cpq(triple(X225,X226,X227),X228) = triple(remove_pqp(X225,X228),remove_slb(X226,X228),X227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
cnf(c_0_25,plain,
( ~ ok(remove_cpq(triple(X1,X2,X3),X4))
| ~ contains_slb(X2,X4)
| ~ strictly_less_than(X4,lookup_slb(X2,X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
contains_slb(esk4_0,esk6_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
cnf(c_0_27,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,lemma,
( less_than(X5,X4)
| ~ check_cpq(triple(X1,X2,X3))
| ~ pair_in_list(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),X4)
| ~ contains_slb(X1,X2)
| ~ less_than(lookup_slb(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
~ strictly_less_than(esk6_0,lookup_slb(esk4_0,esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26])]) ).
cnf(c_0_32,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,lemma,
! [X261,X262,X263,X264,X265] :
( ~ pair_in_list(X262,X264,X265)
| ~ strictly_less_than(X264,X265)
| ~ ok(remove_cpq(triple(X261,X262,X263),X264))
| pair_in_list(remove_slb(X262,X264),X264,X265) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l30_li3132])]) ).
cnf(c_0_34,lemma,
( less_than(X1,X2)
| ~ check_cpq(remove_cpq(triple(X3,X4,X5),X6))
| ~ pair_in_list(remove_slb(X4,X6),X2,X1)
| ~ contains_slb(X4,X6)
| ~ less_than(lookup_slb(X4,X6),X6) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
check_cpq(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,negated_conjecture,
less_than(lookup_slb(esk4_0,esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,lemma,
( pair_in_list(remove_slb(X1,X2),X2,X3)
| ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X2,X3)
| ~ ok(remove_cpq(triple(X4,X1,X5),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( less_than(X1,X2)
| ~ pair_in_list(remove_slb(esk4_0,esk6_0),X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26]),c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
( pair_in_list(remove_slb(esk4_0,esk6_0),esk6_0,X1)
| ~ pair_in_list(esk4_0,esk6_0,X1)
| ~ strictly_less_than(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_40,negated_conjecture,
( less_than(X1,esk6_0)
| ~ pair_in_list(esk4_0,esk6_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]) ).
cnf(c_0_41,negated_conjecture,
pair_in_list(esk4_0,esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,negated_conjecture,
~ less_than(esk7_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV394+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 : n018.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 05:07:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.38/1.75 % Version : CSE_E---1.7
% 1.38/1.75 % Problem : theBenchmark.p
% 1.38/1.75 % SZS status Theorem for theBenchmark.p
% 1.38/1.75 % SZS output start CNFRefutation
% See solution above
% 1.38/1.75 % Total time : 1.373s
%------------------------------------------------------------------------------