%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC190+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n003.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 05:18:40 PM UTC 2026
% Result : Theorem 1.66s 1.83s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 190 ( 51 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 216 ( 84 ~; 81 |; 22 &)
% ( 1 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1
| X5 = X6 ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X3,X10) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1
| X5 = X6 ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X3,X10) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_9,negated_conjecture,
! [X477] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0
& esk52_0 != esk53_0
& ssItem(esk56_0)
& ( ~ ssItem(X477)
| esk56_0 = X477
| ~ memberP(esk50_0,X477) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_10,plain,
! [X439,X440,X441] :
( ~ ssList(X439)
| ~ ssList(X440)
| ~ ssList(X441)
| app(app(X439,X440),X441) = app(X439,app(X440,X441)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_11,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X328,X329] :
( ~ ssList(X328)
| ~ ssItem(X329)
| ssList(cons(X329,X328)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_15,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,nil),cons(esk53_0,nil))),esk55_0) = esk48_0
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_18,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,nil),cons(esk53_0,nil))),esk55_0) = esk48_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_20,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_21,plain,
! [X437,X438] :
( ~ ssList(X437)
| ~ ssItem(X438)
| cons(X438,X437) = app(cons(X438,nil),X437) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_22,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,nil),cons(esk53_0,nil))),esk55_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_17]),c_0_20])]) ).
cnf(c_0_23,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,cons(esk53_0,nil))),esk55_0) = esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
app(app(esk54_0,cons(esk52_0,cons(esk53_0,nil))),esk55_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk53_0,nil)),esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_25]),c_0_26]),c_0_13])]) ).
cnf(c_0_28,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk53_0,nil)),esk55_0)) = esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_20])]) ).
fof(c_0_29,plain,
! [X349,X350,X351] :
( ~ ssList(X349)
| ~ ssList(X350)
| ~ ssItem(X351)
| cons(X351,app(X350,X349)) = app(cons(X351,X350),X349) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_30,negated_conjecture,
app(esk54_0,app(cons(esk52_0,cons(esk53_0,nil)),esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_31,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk53_0,nil),esk55_0)) = esk48_0
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_26])]) ).
fof(c_0_33,plain,
! [X347,X348] :
( ~ ssList(X347)
| ~ ssList(X348)
| ssList(app(X347,X348)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_34,plain,
! [X228,X229,X232,X233] :
( ( ssList(esk3_2(X228,X229))
| ~ memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) )
& ( ssList(esk4_2(X228,X229))
| ~ memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) )
& ( app(esk3_2(X228,X229),cons(X229,esk4_2(X228,X229))) = X228
| ~ memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) )
& ( ~ ssList(X232)
| ~ ssList(X233)
| app(X232,cons(X229,X233)) != X228
| memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_35,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(cons(esk53_0,nil),esk55_0))) = esk48_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26]),c_0_20])]) ).
cnf(c_0_36,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk53_0,nil),esk55_0)) = esk48_0
| ~ ssList(app(esk54_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_37,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
app(esk54_0,cons(esk52_0,app(cons(esk53_0,nil),esk55_0))) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_40,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk53_0,nil),esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_13])]) ).
cnf(c_0_41,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
app(esk54_0,cons(esk52_0,cons(esk53_0,esk55_0))) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_26]),c_0_18])]) ).
cnf(c_0_43,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_44,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk53_0,nil),esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_16]),c_0_17]),c_0_20])]) ).
cnf(c_0_45,negated_conjecture,
( esk56_0 = X1
| ~ ssItem(X1)
| ~ memberP(esk50_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_46,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_47,negated_conjecture,
( memberP(esk48_0,esk52_0)
| ~ ssList(cons(esk53_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_13]),c_0_20])]) ).
cnf(c_0_48,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_23]),c_0_26]),c_0_18])]) ).
cnf(c_0_49,negated_conjecture,
( esk56_0 = X1
| ~ memberP(esk48_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_16]),c_0_26]),c_0_18])]) ).
cnf(c_0_51,negated_conjecture,
( memberP(esk48_0,esk53_0)
| ~ ssList(app(esk54_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_43]),c_0_26]),c_0_18])]) ).
cnf(c_0_52,negated_conjecture,
esk56_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_20])]) ).
cnf(c_0_53,negated_conjecture,
( memberP(esk48_0,esk53_0)
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_37]),c_0_13])]) ).
cnf(c_0_54,negated_conjecture,
( esk52_0 = X1
| ~ memberP(esk48_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_49,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
memberP(esk48_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_16]),c_0_17]),c_0_20])]) ).
cnf(c_0_56,negated_conjecture,
esk52_0 != esk53_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_18])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC190+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 04:33:11 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.66/1.83 % Version : CSE_E---1.7
% 1.66/1.83 % Problem : theBenchmark.p
% 1.66/1.83 % SZS status Theorem for theBenchmark.p
% 1.66/1.83 % SZS output start CNFRefutation
% See solution above
% 1.66/1.83 % Total time : 1.375s
%------------------------------------------------------------------------------