%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC182+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n004.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 05:18:38 PM UTC 2026
% Result : Theorem 1.33s 1.72s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 120 ( 39 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 129 ( 48 ~; 42 |; 16 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X3
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ( ~ memberP(X6,X5)
& ~ memberP(X7,X5) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X3
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ( ~ memberP(X6,X5)
& ~ memberP(X7,X5) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_7,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& nil = esk50_0
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& ssList(esk53_0)
& ssList(esk54_0)
& app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
& ( memberP(esk53_0,esk52_0)
| memberP(esk54_0,esk52_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_8,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
nil = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X436,X437] :
( ( nil = X437
| nil != app(X436,X437)
| ~ ssList(X437)
| ~ ssList(X436) )
& ( nil = X436
| nil != app(X436,X437)
| ~ ssList(X437)
| ~ ssList(X436) )
& ( nil != X437
| nil != X436
| nil = app(X436,X437)
| ~ ssList(X437)
| ~ ssList(X436) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_11,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
esk48_0 = nil,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = nil,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_16,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssList(X342)
| ssList(app(X341,X342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_17,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = nil
| ~ ssList(app(esk53_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_21,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| ssList(cons(X323,X322)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_22,negated_conjecture,
( esk54_0 = nil
| ~ ssList(app(esk53_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15])]) ).
cnf(c_0_23,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = nil
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_26,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( esk54_0 = nil
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
app(esk53_0,cons(esk52_0,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
fof(c_0_29,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_30,negated_conjecture,
( memberP(esk53_0,esk52_0)
| memberP(esk54_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_31,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,negated_conjecture,
( esk53_0 = nil
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_28]),c_0_20])]) ).
fof(c_0_33,plain,
! [X368] :
( ~ ssItem(X368)
| ~ memberP(nil,X368) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
cnf(c_0_34,negated_conjecture,
( memberP(nil,esk52_0)
| memberP(esk53_0,esk52_0) ),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_36,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
memberP(nil,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC182+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 04:31:32 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.33/1.72 % Version : CSE_E---1.7
% 1.33/1.72 % Problem : theBenchmark.p
% 1.33/1.72 % SZS status Theorem for theBenchmark.p
% 1.33/1.72 % SZS output start CNFRefutation
% See solution above
% 1.33/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------