%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV399+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 : n008.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 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 7 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 85 ( 35 ~; 30 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l35_co,conjecture,
! [X1] :
( ? [X2,X3] :
( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X3) )
=> ! [X4] :
? [X5,X6] :
( pair_in_list(update_slb(X1,X4),X5,X6)
& strictly_less_than(X5,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l35_co) ).
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(l35_li3839,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l35_li3839) ).
fof(l35_li3637,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& less_than(X4,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l35_li3637) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(transitivity,axiom,
! [X1,X2,X3] :
( ( less_than(X1,X2)
& less_than(X2,X3) )
=> less_than(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',transitivity) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ? [X2,X3] :
( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X3) )
=> ! [X4] :
? [X5,X6] :
( pair_in_list(update_slb(X1,X4),X5,X6)
& strictly_less_than(X5,X6) ) ),
inference(assume_negation,[status(cth)],[l35_co]) ).
fof(c_0_7,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_8,lemma,
! [X119,X120,X121,X122] :
( ~ pair_in_list(X119,X120,X121)
| ~ strictly_less_than(X121,X122)
| pair_in_list(update_slb(X119,X122),X120,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l35_li3839])]) ).
fof(c_0_9,negated_conjecture,
! [X127,X128] :
( pair_in_list(esk1_0,esk2_0,esk3_0)
& strictly_less_than(esk2_0,esk3_0)
& ( ~ pair_in_list(update_slb(esk1_0,esk4_0),X127,X128)
| ~ strictly_less_than(X127,X128) ) ),
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,lemma,
! [X115,X116,X117,X118] :
( ~ pair_in_list(X115,X116,X117)
| ~ less_than(X118,X117)
| pair_in_list(update_slb(X115,X118),X116,X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l35_li3637])]) ).
fof(c_0_11,plain,
! [X74,X75] :
( ( less_than(X74,X75)
| ~ strictly_less_than(X74,X75) )
& ( ~ less_than(X75,X74)
| ~ strictly_less_than(X74,X75) )
& ( ~ less_than(X74,X75)
| less_than(X75,X74)
| strictly_less_than(X74,X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,lemma,
( pair_in_list(update_slb(X1,X4),X2,X4)
| ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
pair_in_list(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X71,X72] :
( less_than(X71,X72)
| less_than(X72,X71) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_15,negated_conjecture,
( ~ pair_in_list(update_slb(esk1_0,esk4_0),X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
( pair_in_list(update_slb(X1,X4),X2,X3)
| ~ pair_in_list(X1,X2,X3)
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X68,X69,X70] :
( ~ less_than(X68,X69)
| ~ less_than(X69,X70)
| less_than(X68,X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
cnf(c_0_18,plain,
( less_than(X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
strictly_less_than(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| ~ strictly_less_than(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( ~ pair_in_list(esk1_0,X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ less_than(esk4_0,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
less_than(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( ~ strictly_less_than(esk2_0,esk4_0)
| ~ strictly_less_than(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_27,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
~ less_than(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_13])]) ).
cnf(c_0_29,negated_conjecture,
( less_than(X1,esk3_0)
| ~ less_than(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
~ strictly_less_than(esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
~ less_than(esk4_0,esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV399+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
% 0.14/0.32 % Computer : n008.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 05:07:13 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------