%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV378+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 : n002.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 05:22:02 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 83 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 82 ( 38 ~; 26 |; 7 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 91 ( 9 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l14_co,conjecture,
! [X1,X2,X3,X4] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l14_co) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax41) ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax40) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
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/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l14_co])]) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(c_0_10,negated_conjecture,
( ~ ok(triple(esk1_0,esk2_0,esk3_0))
& ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X203,X204,X205] :
( ok(triple(X203,X204,X205))
| X205 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_12,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
cnf(c_0_13,negated_conjecture,
~ ok(triple(esk1_0,esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,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_16,plain,
! [X201,X202] : ~ ok(triple(X201,X202,bad)),
inference(variable_rename,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X218,X219,X220,X221] :
( ~ contains_slb(X219,X221)
| ~ strictly_less_than(X221,lookup_slb(X219,X221))
| remove_cpq(triple(X218,X219,X220),X221) = triple(remove_pqp(X218,X221),remove_slb(X219,X221),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_18,negated_conjecture,
ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
esk3_0 = bad,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,plain,
! [X210,X211,X212,X213] :
( contains_slb(X211,X213)
| remove_cpq(triple(X210,X211,X212),X213) = triple(X210,X211,bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
fof(c_0_21,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_22,plain,
! [X214,X215,X216,X217] :
( ~ contains_slb(X215,X217)
| ~ less_than(lookup_slb(X215,X217),X217)
| remove_cpq(triple(X214,X215,X216),X217) = triple(remove_pqp(X214,X217),remove_slb(X215,X217),X216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
cnf(c_0_23,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,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_17]) ).
cnf(c_0_25,negated_conjecture,
ok(remove_cpq(triple(esk1_0,esk2_0,bad),esk4_0)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( contains_slb(X1,X2)
| remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,plain,
! [X133,X134] :
( ( less_than(X133,X134)
| ~ strictly_less_than(X133,X134) )
& ( ~ less_than(X134,X133)
| ~ strictly_less_than(X133,X134) )
& ( ~ less_than(X133,X134)
| less_than(X134,X133)
| strictly_less_than(X133,X134) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_28,plain,
! [X130,X131] :
( less_than(X130,X131)
| less_than(X131,X130) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_29,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_22]) ).
cnf(c_0_30,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_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
contains_slb(esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_32,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( ~ ok(remove_cpq(triple(X1,X2,bad),X3))
| ~ contains_slb(X2,X3)
| ~ less_than(lookup_slb(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
~ strictly_less_than(esk4_0,lookup_slb(esk2_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_31])]) ).
cnf(c_0_36,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
~ less_than(lookup_slb(esk2_0,esk4_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_31])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV378+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 : n002.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 05:05:16 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % 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 : 1.369s
%------------------------------------------------------------------------------