%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC315+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 : n005.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 05:19:09 PM UTC 2026
% Result : Theorem 1.44s 1.76s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 13 unt; 0 def)
% Number of atoms : 199 ( 109 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 209 ( 73 ~; 90 |; 25 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) = X1 ) )
& ( nil != X2
| nil = X1 ) )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) = X1 ) )
& ( nil != X2
| nil = X1 ) )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_8,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( nil = esk50_0
| nil != esk51_0 )
& ( nil = esk49_0
| ssItem(esk52_0) )
& ( nil != esk48_0
| ssItem(esk52_0) )
& ( nil = esk49_0
| ssList(esk53_0) )
& ( nil != esk48_0
| ssList(esk53_0) )
& ( nil = esk49_0
| app(cons(esk52_0,nil),esk53_0) = esk49_0 )
& ( nil != esk48_0
| app(cons(esk52_0,nil),esk53_0) = esk49_0 )
& ( nil = esk49_0
| app(esk53_0,cons(esk52_0,nil)) != esk48_0 )
& ( nil != esk48_0
| app(esk53_0,cons(esk52_0,nil)) != esk48_0 )
& ( ssItem(esk54_0)
| ~ neq(esk51_0,nil) )
& ( ssList(esk55_0)
| ~ neq(esk51_0,nil) )
& ( app(cons(esk54_0,nil),esk55_0) = esk51_0
| ~ neq(esk51_0,nil) )
& ( app(esk55_0,cons(esk54_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,plain,
! [X322,X323] :
( ( ~ neq(X322,X323)
| X322 != X323
| ~ ssList(X323)
| ~ ssList(X322) )
& ( X322 = X323
| neq(X322,X323)
| ~ ssList(X323)
| ~ ssList(X322) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_10,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( app(cons(esk54_0,nil),esk55_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_16,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_17,negated_conjecture,
( ssItem(esk54_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( ssList(esk55_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
( nil = esk49_0
| app(cons(esk52_0,nil),esk53_0) = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( nil = esk49_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( nil = esk49_0
| ssList(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_22,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])])]) ).
cnf(c_0_23,negated_conjecture,
( app(cons(esk54_0,nil),esk55_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( esk51_0 = nil
| ssItem(esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_26,negated_conjecture,
( esk51_0 = nil
| ssList(esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk51_0
| esk51_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_11]),c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( esk51_0 = nil
| ssItem(esk52_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( esk51_0 = nil
| ssList(esk53_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( app(esk55_0,cons(esk54_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,negated_conjecture,
( cons(esk54_0,esk55_0) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]) ).
cnf(c_0_34,negated_conjecture,
( cons(esk52_0,esk53_0) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_28]),c_0_29]) ).
fof(c_0_35,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssItem(X342)
| tl(cons(X342,X341)) = X341 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_36,negated_conjecture,
( app(esk55_0,cons(esk54_0,nil)) = esk48_0
| ~ neq(esk51_0,nil) ),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( hd(esk51_0) = esk54_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_25]),c_0_26]) ).
cnf(c_0_38,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_28]),c_0_29]) ).
cnf(c_0_39,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( app(esk55_0,cons(esk54_0,nil)) = esk48_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_41,negated_conjecture,
( esk51_0 = nil
| esk54_0 = esk52_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( tl(esk51_0) = esk55_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_25]),c_0_26]) ).
cnf(c_0_43,negated_conjecture,
( tl(esk51_0) = esk53_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_34]),c_0_28]),c_0_29]) ).
cnf(c_0_44,negated_conjecture,
( nil = esk49_0
| app(esk53_0,cons(esk52_0,nil)) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_45,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_46,negated_conjecture,
( app(esk55_0,cons(esk52_0,nil)) = esk48_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( esk51_0 = nil
| esk55_0 = esk53_0 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( esk51_0 = nil
| app(esk53_0,cons(esk52_0,nil)) != esk48_0 ),
inference(rw,[status(thm)],[c_0_44,c_0_11]) ).
cnf(c_0_49,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_50,negated_conjecture,
( esk48_0 = nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[c_0_45,c_0_31]) ).
cnf(c_0_51,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk51_0
| esk48_0 != nil ),
inference(rw,[status(thm)],[c_0_49,c_0_11]) ).
cnf(c_0_53,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_54,negated_conjecture,
( ssList(esk53_0)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_55,negated_conjecture,
( ssItem(esk52_0)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_56,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_57,negated_conjecture,
app(cons(esk52_0,nil),esk53_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_51]),c_0_53])]) ).
cnf(c_0_58,negated_conjecture,
ssList(esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_53])]) ).
cnf(c_0_59,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_53])]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,negated_conjecture,
cons(esk52_0,esk53_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_58]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC315+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
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:53:00 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.44/1.76 % Version : CSE_E---1.7
% 1.44/1.76 % Problem : theBenchmark.p
% 1.44/1.76 % SZS status Theorem for theBenchmark.p
% 1.44/1.76 % SZS output start CNFRefutation
% See solution above
% 1.44/1.76 % Total time : 1.369s
%------------------------------------------------------------------------------