%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC067+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 : n031.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 05:18:07 PM UTC 2026
% Result : Theorem 1.42s 1.74s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 230 ( 67 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 296 ( 111 ~; 107 |; 57 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 35 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& lt(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& lt(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X15] :
( ssList(X15)
& neq(X15,nil)
& segmentP(X2,X15)
& segmentP(X1,X15) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
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(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& lt(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& lt(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X15] :
( ssList(X15)
& neq(X15,nil)
& segmentP(X2,X15)
& segmentP(X1,X15) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_7,negated_conjecture,
! [X484,X485,X486,X487,X488,X489,X490,X491,X492] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& ssList(esk53_0)
& app(app(esk52_0,esk50_0),esk53_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X484)
| ~ ssList(X485)
| app(X485,cons(X484,nil)) != esk52_0
| ~ ssItem(X486)
| ~ ssList(X487)
| app(cons(X486,nil),X487) != esk50_0
| ~ lt(X484,X486) )
& ( ~ ssItem(X488)
| ~ ssList(X489)
| app(cons(X488,nil),X489) != esk53_0
| ~ ssItem(X490)
| ~ ssList(X491)
| app(X491,cons(X490,nil)) != esk50_0
| ~ lt(X490,X488) )
& ( nil = esk51_0
| nil != esk50_0 )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X492)
| ~ neq(X492,nil)
| ~ segmentP(esk49_0,X492)
| ~ segmentP(esk48_0,X492)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X492)
| ~ neq(X492,nil)
| ~ segmentP(esk49_0,X492)
| ~ segmentP(esk48_0,X492)
| nil != esk48_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_8,plain,
! [X255,X256,X259,X260] :
( ( ssList(esk8_2(X255,X256))
| ~ segmentP(X255,X256)
| ~ ssList(X256)
| ~ ssList(X255) )
& ( ssList(esk9_2(X255,X256))
| ~ segmentP(X255,X256)
| ~ ssList(X256)
| ~ ssList(X255) )
& ( app(app(esk8_2(X255,X256),X256),esk9_2(X255,X256)) = X255
| ~ segmentP(X255,X256)
| ~ ssList(X256)
| ~ ssList(X255) )
& ( ~ ssList(X259)
| ~ ssList(X260)
| app(app(X259,X256),X260) != X255
| segmentP(X255,X256)
| ~ ssList(X256)
| ~ ssList(X255) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
cnf(c_0_9,negated_conjecture,
( nil = esk49_0
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X416] :
( ~ ssList(X416)
| segmentP(X416,X416) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_12,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
app(app(esk52_0,esk50_0),esk53_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk50_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_19,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
app(app(esk52_0,esk50_0),esk53_0) = esk49_0,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk49_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
segmentP(esk49_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_18]),c_0_22]),c_0_23])]) ).
fof(c_0_26,plain,
! [X336,X337] :
( ( ~ neq(X336,X337)
| X336 != X337
| ~ ssList(X337)
| ~ ssList(X336) )
& ( X336 = X337
| neq(X336,X337)
| ~ ssList(X337)
| ~ ssList(X336) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_27,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,negated_conjecture,
( esk49_0 = nil
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_32,negated_conjecture,
( esk49_0 = nil
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( esk50_0 != nil
| ~ segmentP(esk50_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_10]),c_0_10]) ).
fof(c_0_34,plain,
! [X422] :
( ( ~ segmentP(nil,X422)
| nil = X422
| ~ ssList(X422) )
& ( nil != X422
| segmentP(nil,X422)
| ~ ssList(X422) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).
cnf(c_0_35,negated_conjecture,
esk49_0 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_18])]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( esk50_0 != nil
| ~ segmentP(esk49_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_18])]) ).
cnf(c_0_37,plain,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
segmentP(nil,esk50_0),
inference(rw,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( esk50_0 != nil
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_25])]) ).
cnf(c_0_41,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18])]) ).
cnf(c_0_42,negated_conjecture,
( neq(esk49_0,nil)
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_39,c_0_10]) ).
cnf(c_0_43,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_35]),c_0_41])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC067+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
% 0.15/0.32 % Computer : n031.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:26:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.42/1.74 % Version : CSE_E---1.7
% 1.42/1.74 % Problem : theBenchmark.p
% 1.42/1.74 % SZS status Theorem for theBenchmark.p
% 1.42/1.74 % SZS output start CNFRefutation
% See solution above
% 1.42/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------