%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC192+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 : 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 05:18:40 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% Number of atoms : 196 ( 64 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 217 ( 74 ~; 82 |; 25 &)
% ( 1 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 50 !; 0 ?)
% 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)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
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(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax14,axiom,
! [X1] :
( ssList(X1)
=> ( equalelemsP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X4,cons(X2,cons(X3,X5))) = X1
=> X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax14) ).
fof(ax73,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(ax74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax74) ).
fof(c_0_9,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)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_10,negated_conjecture,
( 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
& ( nil = esk51_0
| ssItem(esk56_0) )
& ( nil = esk50_0
| ssItem(esk56_0) )
& ( nil = esk51_0
| cons(esk56_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk56_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk56_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk56_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
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_10]) ).
cnf(c_0_12,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X437,X438,X439] :
( ~ ssList(X437)
| ~ ssList(X438)
| ~ ssList(X439)
| app(app(X437,X438),X439) = app(X437,app(X438,X439)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_14,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_18,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,nil),cons(esk53_0,nil))),esk55_0) = esk50_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_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_21,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,nil),cons(esk53_0,nil))),esk55_0) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_23,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_24,plain,
! [X435,X436] :
( ~ ssList(X435)
| ~ ssItem(X436)
| cons(X436,X435) = app(cons(X436,nil),X435) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_25,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,nil),cons(esk53_0,nil))),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_20]),c_0_23])]) ).
cnf(c_0_26,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,cons(esk53_0,nil))),esk55_0) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
app(app(esk54_0,cons(esk52_0,cons(esk53_0,nil))),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk53_0,nil)),esk55_0)) = esk50_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_15,c_0_28]),c_0_29]),c_0_16])]) ).
cnf(c_0_31,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk53_0,nil)),esk55_0)) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_23])]) ).
fof(c_0_32,plain,
! [X347,X348,X349] :
( ~ ssList(X347)
| ~ ssList(X348)
| ~ ssItem(X349)
| cons(X349,app(X348,X347)) = app(cons(X349,X348),X347) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_33,negated_conjecture,
app(esk54_0,app(cons(esk52_0,cons(esk53_0,nil)),esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_34,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X315,X316,X317,X318,X319] :
( ( ~ equalelemsP(X315)
| ~ ssItem(X316)
| ~ ssItem(X317)
| ~ ssList(X318)
| ~ ssList(X319)
| app(X318,cons(X316,cons(X317,X319))) != X315
| X316 = X317
| ~ ssList(X315) )
& ( ssItem(esk40_1(X315))
| equalelemsP(X315)
| ~ ssList(X315) )
& ( ssItem(esk41_1(X315))
| equalelemsP(X315)
| ~ ssList(X315) )
& ( ssList(esk42_1(X315))
| equalelemsP(X315)
| ~ ssList(X315) )
& ( ssList(esk43_1(X315))
| equalelemsP(X315)
| ~ ssList(X315) )
& ( app(esk42_1(X315),cons(esk40_1(X315),cons(esk41_1(X315),esk43_1(X315)))) = X315
| equalelemsP(X315)
| ~ ssList(X315) )
& ( esk40_1(X315) != esk41_1(X315)
| equalelemsP(X315)
| ~ ssList(X315) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])])])])]) ).
cnf(c_0_36,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(cons(esk53_0,nil),esk55_0))) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_23])]) ).
fof(c_0_37,plain,
! [X421] :
( ~ ssItem(X421)
| equalelemsP(cons(X421,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])]) ).
cnf(c_0_38,plain,
( X2 = X3
| ~ equalelemsP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| app(X4,cons(X2,cons(X3,X5))) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
app(esk54_0,cons(esk52_0,app(cons(esk53_0,nil),esk55_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_40,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( nil = esk50_0
| cons(esk56_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,negated_conjecture,
( nil = esk50_0
| ssItem(esk56_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_44,plain,
( X1 = X2
| ~ equalelemsP(app(X3,cons(X1,cons(X2,X4))))
| ~ ssList(app(X3,cons(X1,cons(X2,X4))))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
app(esk54_0,cons(esk52_0,cons(esk53_0,esk55_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_26]),c_0_29]),c_0_21])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_40,c_0_12]) ).
cnf(c_0_47,negated_conjecture,
esk52_0 != esk53_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_48,negated_conjecture,
( esk50_0 = nil
| equalelemsP(esk50_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_49,negated_conjecture,
~ equalelemsP(esk50_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_29]),c_0_16]),c_0_21]),c_0_23])]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
esk50_0 = nil,
inference(sr,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,plain,
equalelemsP(nil),
inference(split_conjunct,[status(thm)],[ax74]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC192+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 : n008.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 04:33:28 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------