%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC166+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 : n029.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 05:18:33 PM UTC 2026
% Result : Theorem 1.62s 1.80s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 21
% Syntax : Number of formulae : 121 ( 29 unt; 0 def)
% Number of atoms : 402 ( 130 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 467 ( 186 ~; 191 |; 25 &)
% ( 5 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 96 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(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
| neq(X5,X6) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
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(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(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
| neq(X5,X6) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_22,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& singletonP(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
& ~ neq(esk52_0,esk53_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_23,plain,
! [X220,X221] :
( ( ~ neq(X220,X221)
| X220 != X221
| ~ ssItem(X221)
| ~ ssItem(X220) )
& ( X220 = X221
| neq(X220,X221)
| ~ ssItem(X221)
| ~ ssItem(X220) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
cnf(c_0_24,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,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_22]) ).
cnf(c_0_29,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
fof(c_0_30,plain,
! [X435,X436,X437] :
( ~ ssList(X435)
| ~ ssList(X436)
| ~ ssList(X437)
| app(app(X435,X436),X437) = app(X435,app(X436,X437)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_31,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk52_0,nil)),esk55_0) = esk48_0,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_34,plain,
! [X324,X325] :
( ~ ssList(X324)
| ~ ssItem(X325)
| ssList(cons(X325,X324)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_35,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,nil),cons(esk52_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_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_38,plain,
! [X433,X434] :
( ~ ssList(X433)
| ~ ssItem(X434)
| cons(X434,X433) = app(cons(X434,nil),X433) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_39,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,nil),cons(esk52_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_36]),c_0_37]),c_0_27])]) ).
cnf(c_0_40,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,cons(esk52_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_39,c_0_40]),c_0_27])]) ).
cnf(c_0_42,negated_conjecture,
app(app(esk54_0,cons(esk52_0,cons(esk52_0,nil))),esk55_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_37]),c_0_27])]) ).
cnf(c_0_43,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk48_0
| ~ ssList(cons(esk52_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_42]),c_0_43]),c_0_33])]) ).
cnf(c_0_45,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk52_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_44,c_0_36]),c_0_27])]) ).
fof(c_0_46,plain,
! [X345,X346,X347] :
( ~ ssList(X345)
| ~ ssList(X346)
| ~ ssItem(X347)
| cons(X347,app(X346,X345)) = app(cons(X347,X346),X345) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_47,negated_conjecture,
app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_36]),c_0_37]),c_0_27])]) ).
cnf(c_0_48,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_49,plain,
! [X233,X234,X236] :
( ( ssList(esk6_2(X233,X234))
| ~ frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( app(X234,esk6_2(X233,X234)) = X233
| ~ frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( ~ ssList(X236)
| app(X234,X236) != X233
| frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(c_0_50,plain,
! [X343,X344] :
( ~ ssList(X343)
| ~ ssList(X344)
| ssList(app(X343,X344)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_51,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(cons(esk52_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_47,c_0_48]),c_0_43]),c_0_27])]) ).
cnf(c_0_52,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
app(esk54_0,cons(esk52_0,app(cons(esk52_0,nil),esk55_0))) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_37]),c_0_27])]) ).
cnf(c_0_55,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_53]) ).
cnf(c_0_56,negated_conjecture,
app(esk54_0,cons(esk52_0,cons(esk52_0,esk55_0))) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_43]),c_0_27])]) ).
fof(c_0_57,plain,
! [X338,X339] :
( ~ ssList(X338)
| ~ ssItem(X339)
| hd(cons(X339,X338)) = X339 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_58,plain,
! [X230,X232] :
( ( ssItem(esk5_1(X230))
| ~ singletonP(X230)
| ~ ssList(X230) )
& ( cons(esk5_1(X230),nil) = X230
| ~ singletonP(X230)
| ~ ssList(X230) )
& ( ~ ssItem(X232)
| cons(X232,nil) != X230
| singletonP(X230)
| ~ ssList(X230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
cnf(c_0_59,negated_conjecture,
( frontsegP(esk48_0,esk54_0)
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_33])]) ).
cnf(c_0_60,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( frontsegP(esk48_0,esk54_0)
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_36]),c_0_27])]) ).
cnf(c_0_64,plain,
( esk5_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_37])]),c_0_62]) ).
cnf(c_0_65,negated_conjecture,
singletonP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_66,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_67,plain,
! [X441,X442] :
( ~ ssList(X441)
| ~ ssList(X442)
| nil = X441
| hd(app(X441,X442)) = hd(X441) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_68,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_69,negated_conjecture,
frontsegP(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_36]),c_0_43]),c_0_27])]) ).
cnf(c_0_70,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_71,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_72,plain,
! [X380,X381,X382,X383] :
( ( X380 = X381
| ~ frontsegP(cons(X380,X382),cons(X381,X383))
| ~ ssList(X383)
| ~ ssList(X382)
| ~ ssItem(X381)
| ~ ssItem(X380) )
& ( frontsegP(X382,X383)
| ~ frontsegP(cons(X380,X382),cons(X381,X383))
| ~ ssList(X383)
| ~ ssList(X382)
| ~ ssItem(X381)
| ~ ssItem(X380) )
& ( X380 != X381
| ~ frontsegP(X382,X383)
| frontsegP(cons(X380,X382),cons(X381,X383))
| ~ ssList(X383)
| ~ ssList(X382)
| ~ ssItem(X381)
| ~ ssItem(X380) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
cnf(c_0_73,plain,
( cons(hd(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
singletonP(esk48_0),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_64]) ).
fof(c_0_76,plain,
! [X426] :
( ~ ssList(X426)
| nil = X426
| cons(hd(X426),tl(X426)) = X426 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_77,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,negated_conjecture,
app(esk54_0,esk6_2(esk48_0,esk54_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_33])]) ).
cnf(c_0_79,negated_conjecture,
ssList(esk6_2(esk48_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_69]),c_0_33]),c_0_70])]) ).
cnf(c_0_80,plain,
( frontsegP(X1,X2)
| ~ frontsegP(cons(X3,X1),cons(X4,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,negated_conjecture,
cons(hd(esk48_0),nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_70])]) ).
cnf(c_0_82,negated_conjecture,
ssItem(hd(esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_74]),c_0_70])]) ).
cnf(c_0_83,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( hd(esk54_0) = hd(esk48_0)
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_33])]) ).
fof(c_0_85,plain,
! [X430,X431,X432] :
( ~ ssList(X430)
| ~ ssList(X431)
| ~ ssList(X432)
| app(X431,X432) != app(X431,X430)
| X432 = X430 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_86,plain,
! [X440] :
( ~ ssList(X440)
| app(X440,nil) = X440 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_87,negated_conjecture,
( frontsegP(nil,X1)
| ~ frontsegP(esk48_0,cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_37]),c_0_82])]) ).
cnf(c_0_88,negated_conjecture,
( cons(hd(esk48_0),tl(esk54_0)) = esk54_0
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_33])]) ).
fof(c_0_89,plain,
! [X340] :
( ~ ssList(X340)
| nil = X340
| ssList(tl(X340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_90,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_92,plain,
! [X385] :
( ( ~ frontsegP(nil,X385)
| nil = X385
| ~ ssList(X385) )
& ( nil != X385
| frontsegP(nil,X385)
| ~ ssList(X385) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
cnf(c_0_93,negated_conjecture,
( esk54_0 = nil
| frontsegP(nil,tl(esk54_0))
| ~ ssList(tl(esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_69]),c_0_82])]) ).
cnf(c_0_94,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_95,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_37])]) ).
cnf(c_0_96,plain,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( esk54_0 = nil
| frontsegP(nil,tl(esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_33])]) ).
cnf(c_0_98,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 != esk48_0
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_56]),c_0_33])]) ).
cnf(c_0_99,negated_conjecture,
( tl(esk54_0) = nil
| esk54_0 = nil
| ~ ssList(tl(esk54_0)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 != esk48_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_36]),c_0_27])]) ).
cnf(c_0_101,negated_conjecture,
( tl(esk54_0) = nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_94]),c_0_33])]) ).
fof(c_0_102,plain,
! [X335,X336] :
( ~ ssList(X335)
| ~ ssItem(X336)
| nil != cons(X336,X335) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_103,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_36]),c_0_43]),c_0_27])]) ).
cnf(c_0_104,negated_conjecture,
( esk54_0 = nil
| esk54_0 = esk48_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_101]),c_0_81]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 = nil ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( esk54_0 = nil
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_27])]) ).
fof(c_0_108,plain,
! [X348] :
( ~ ssList(X348)
| app(nil,X348) = X348 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_109,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_36]),c_0_43]),c_0_27])]) ).
cnf(c_0_110,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_111,negated_conjecture,
app(nil,cons(esk52_0,cons(esk52_0,esk55_0))) = esk48_0,
inference(rw,[status(thm)],[c_0_56,c_0_109]) ).
fof(c_0_112,plain,
! [X328,X329,X330,X331] :
( ( X330 = X331
| cons(X330,X328) != cons(X331,X329)
| ~ ssItem(X331)
| ~ ssItem(X330)
| ~ ssList(X329)
| ~ ssList(X328) )
& ( X329 = X328
| cons(X330,X328) != cons(X331,X329)
| ~ ssItem(X331)
| ~ ssItem(X330)
| ~ ssList(X329)
| ~ ssList(X328) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
cnf(c_0_113,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_114,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_115,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_36]),c_0_27])]) ).
cnf(c_0_116,negated_conjecture,
( X1 = nil
| cons(X2,X1) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_81]),c_0_37]),c_0_82])]) ).
cnf(c_0_117,negated_conjecture,
cons(esk52_0,cons(esk52_0,esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_36]),c_0_43]),c_0_27])]) ).
cnf(c_0_118,negated_conjecture,
( cons(esk52_0,esk55_0) = nil
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_27])]) ).
cnf(c_0_119,negated_conjecture,
cons(esk52_0,esk55_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_36]),c_0_43]),c_0_27])]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_119]),c_0_43]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC166+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:30:44 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.62/1.80 % Version : CSE_E---1.7
% 1.62/1.80 % Problem : theBenchmark.p
% 1.62/1.80 % SZS status Theorem for theBenchmark.p
% 1.62/1.80 % SZS output start CNFRefutation
% See solution above
% 1.62/1.80 % Total time : 1.372s
%------------------------------------------------------------------------------