%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC052+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 : n013.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 05:18:04 PM UTC 2026
% Result : Theorem 1.49s 1.78s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 11 unt; 0 def)
% Number of atoms : 233 ( 61 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 292 ( 118 ~; 124 |; 34 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 30 !; 5 ?)
% 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] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X3,X5) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X6] :
( ssList(X6)
& neq(X6,nil)
& segmentP(X2,X6)
& segmentP(X1,X6) ) ) ) ) ) ) ),
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
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] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X3,X5) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X6] :
( ssList(X6)
& neq(X6,nil)
& segmentP(X2,X6)
& segmentP(X1,X6) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_8,negated_conjecture,
! [X465] :
( 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 )
& ( ssList(esk52_0)
| ~ neq(esk51_0,nil) )
& ( neq(esk52_0,nil)
| ~ neq(esk51_0,nil) )
& ( frontsegP(esk51_0,esk52_0)
| ~ neq(esk51_0,nil) )
& ( frontsegP(esk50_0,esk52_0)
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X465)
| ~ neq(X465,nil)
| ~ segmentP(esk49_0,X465)
| ~ segmentP(esk48_0,X465)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X465)
| ~ neq(X465,nil)
| ~ segmentP(esk49_0,X465)
| ~ segmentP(esk48_0,X465)
| 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_7])])])])]) ).
fof(c_0_9,plain,
! [X237,X238,X241,X242] :
( ( ssList(esk8_2(X237,X238))
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ssList(esk9_2(X237,X238))
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(app(esk8_2(X237,X238),X238),esk9_2(X237,X238)) = X237
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X241)
| ~ ssList(X242)
| app(app(X241,X238),X242) != X237
| segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) ) ),
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_10,negated_conjecture,
( frontsegP(esk50_0,esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( neq(esk49_0,nil)
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,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_9]) ).
fof(c_0_15,plain,
! [X344] :
( ~ ssList(X344)
| app(nil,X344) = X344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_16,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssList(X340)
| ssList(app(X339,X340)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_17,plain,
! [X229,X230,X232] :
( ( ssList(esk6_2(X229,X230))
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( app(X230,esk6_2(X229,X230)) = X229
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( ~ ssList(X232)
| app(X230,X232) != X229
| frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_18,negated_conjecture,
( frontsegP(esk48_0,esk52_0)
| ~ neq(esk51_0,nil) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( esk51_0 = nil
| neq(esk51_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( ssList(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( frontsegP(esk51_0,esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,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_14]) ).
cnf(c_0_24,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_26,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk48_0,esk52_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
( esk51_0 = nil
| ssList(esk52_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_31,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,esk52_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_34,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_8]) ).
fof(c_0_35,plain,
! [X403] :
( ~ ssList(X403)
| segmentP(X403,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_36,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_8]) ).
cnf(c_0_37,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_38,negated_conjecture,
( app(esk52_0,esk6_2(esk48_0,esk52_0)) = esk48_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( esk51_0 = nil
| ssList(esk6_2(esk48_0,esk52_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( neq(esk52_0,nil)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,negated_conjecture,
( app(esk52_0,esk6_2(esk51_0,esk52_0)) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_33])]),c_0_30]) ).
cnf(c_0_42,negated_conjecture,
( esk51_0 = nil
| ssList(esk6_2(esk51_0,esk52_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_30]) ).
cnf(c_0_43,negated_conjecture,
( esk48_0 != nil
| ~ segmentP(esk48_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_44,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
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,
( esk51_0 = nil
| ~ segmentP(esk48_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_13]),c_0_13]) ).
cnf(c_0_47,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,esk52_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_30]),c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( esk51_0 = nil
| neq(esk52_0,nil) ),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_49,negated_conjecture,
( esk51_0 = nil
| segmentP(esk51_0,esk52_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41]),c_0_30]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( esk48_0 != nil
| ~ segmentP(esk51_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_25]),c_0_29])]) ).
cnf(c_0_51,negated_conjecture,
( esk48_0 = nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[c_0_45,c_0_11]) ).
cnf(c_0_52,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_30]),c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_54,negated_conjecture,
( esk48_0 != nil
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_44]),c_0_33])]) ).
cnf(c_0_55,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_56,negated_conjecture,
( neq(esk51_0,nil)
| esk48_0 != nil ),
inference(rw,[status(thm)],[c_0_53,c_0_13]) ).
cnf(c_0_57,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_52]),c_0_55])]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC052+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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 04:18:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.49/1.78 % Version : CSE_E---1.7
% 1.49/1.78 % Problem : theBenchmark.p
% 1.49/1.78 % SZS status Theorem for theBenchmark.p
% 1.49/1.78 % SZS output start CNFRefutation
% See solution above
% 1.49/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------