%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV409+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n015.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 1.37s 1.75s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 107 ( 41 ~; 42 |; 17 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l45_co,conjecture,
! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).
fof(l45_li4647,lemma,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(l45_l48,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X4)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l45_l49,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X4)
& less_than(X4,X3) )
=> ? [X5] :
( pair_in_list(update_slb(X1,X4),X2,X5)
& less_than(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
inference(assume_negation,[status(cth)],[l45_co]) ).
fof(c_0_7,lemma,
! [X116,X117] :
( ~ contains_slb(X116,X117)
| pair_in_list(X116,X117,esk1_2(X116,X117)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])]) ).
fof(c_0_8,negated_conjecture,
! [X131] :
( contains_slb(esk3_0,esk4_0)
& strictly_less_than(esk4_0,esk5_0)
& ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0)
& ( ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X131)
| ~ less_than(esk5_0,X131) ) ),
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,
! [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_10,lemma,
! [X119,X120,X121,X122] :
( ~ pair_in_list(X119,X120,X121)
| ~ strictly_less_than(X120,X122)
| ~ strictly_less_than(X121,X122)
| pair_in_list(update_slb(X119,X122),X120,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l48])]) ).
cnf(c_0_11,lemma,
( pair_in_list(X1,X2,esk1_2(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
contains_slb(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X75,X76] :
( ( less_than(X75,X76)
| ~ strictly_less_than(X75,X76) )
& ( ~ less_than(X76,X75)
| ~ strictly_less_than(X75,X76) )
& ( ~ less_than(X75,X76)
| less_than(X76,X75)
| strictly_less_than(X75,X76) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,plain,
! [X72,X73] :
( less_than(X72,X73)
| less_than(X73,X72) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_15,lemma,
( pair_in_list(update_slb(X1,X4),X2,X4)
| ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X2,X4)
| ~ strictly_less_than(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
pair_in_list(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,lemma,
! [X123,X124,X125,X126] :
( ( pair_in_list(update_slb(X123,X126),X124,esk2_4(X123,X124,X125,X126))
| ~ pair_in_list(X123,X124,X125)
| ~ strictly_less_than(X124,X126)
| ~ less_than(X126,X125) )
& ( less_than(X126,esk2_4(X123,X124,X125,X126))
| ~ pair_in_list(X123,X124,X125)
| ~ strictly_less_than(X124,X126)
| ~ less_than(X126,X125) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l49])])])]) ).
cnf(c_0_20,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk4_0,X1)
| ~ strictly_less_than(esk1_2(esk3_0,esk4_0),X1)
| ~ strictly_less_than(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,lemma,
( pair_in_list(update_slb(X1,X2),X3,esk2_4(X1,X3,X4,X2))
| ~ pair_in_list(X1,X3,X4)
| ~ strictly_less_than(X3,X2)
| ~ less_than(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk4_0,X1)
| less_than(X1,esk1_2(esk3_0,esk4_0))
| ~ strictly_less_than(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
strictly_less_than(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,lemma,
( less_than(X1,esk2_4(X2,X3,X4,X1))
| ~ pair_in_list(X2,X3,X4)
| ~ strictly_less_than(X3,X1)
| ~ less_than(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk4_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),X1))
| ~ strictly_less_than(esk4_0,X1)
| ~ less_than(X1,esk1_2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
less_than(esk5_0,esk1_2(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( less_than(X1,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),X1))
| ~ strictly_less_than(esk4_0,X1)
| ~ less_than(X1,esk1_2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X1)
| ~ less_than(esk5_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,negated_conjecture,
pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
less_than(esk5_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_24])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV409+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n015.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 05:06:32 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.37/1.75 % Version : CSE_E---1.7
% 1.37/1.75 % Problem : theBenchmark.p
% 1.37/1.75 % SZS status Theorem for theBenchmark.p
% 1.37/1.75 % SZS output start CNFRefutation
% See solution above
% 1.37/1.75 % Total time : 1.370s
%------------------------------------------------------------------------------