%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC229+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 : n009.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 05:18:48 PM UTC 2026
% Result : Theorem 3.07s 2.96s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 14 unt; 0 def)
% Number of atoms : 266 ( 65 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 340 ( 142 ~; 133 |; 31 &)
% ( 3 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 98 ( 0 sgn 53 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_13,plain,
! [X438,X439] :
( ( nil = X439
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil = X438
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil != X439
| nil != X438
| nil = app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_14,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])])]) ).
fof(c_0_15,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])])]) ).
fof(c_0_16,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_17,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_20,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]),c_0_18])]) ).
fof(c_0_24,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_25,negated_conjecture,
! [X468,X469,X470] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& segmentP(esk51_0,esk50_0)
& nil != esk48_0
& ( ssItem(esk52_3(X468,X469,X470))
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk48_0
| ~ ssList(X469)
| ~ ssItem(X468) )
& ( memberP(X469,esk52_3(X468,X469,X470))
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk48_0
| ~ ssList(X469)
| ~ ssItem(X468) )
& ( memberP(X470,esk52_3(X468,X469,X470))
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk48_0
| ~ ssList(X469)
| ~ ssItem(X468) )
& ( leq(X468,esk52_3(X468,X469,X470))
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk48_0
| ~ ssList(X469)
| ~ ssItem(X468) )
& ( ~ leq(esk52_3(X468,X469,X470),X468)
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk48_0
| ~ ssList(X469)
| ~ ssItem(X468) )
& ( singletonP(esk50_0)
| ~ neq(esk51_0,nil) ) ),
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_19])])])])]) ).
fof(c_0_26,plain,
! [X348] :
( ~ ssList(X348)
| app(nil,X348) = X348 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_27,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,plain,
( app(cons(X1,nil),nil) = cons(X1,nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_18])]) ).
fof(c_0_29,plain,
! [X370] :
( ~ ssItem(X370)
| ~ memberP(nil,X370) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
cnf(c_0_30,negated_conjecture,
( memberP(X1,esk52_3(X2,X3,X1))
| ~ ssList(X1)
| app(app(X3,cons(X2,nil)),X1) != esk48_0
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18])]) ).
cnf(c_0_33,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( memberP(X1,esk52_3(X2,nil,X1))
| app(cons(X2,nil),X1) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_18])]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
( app(cons(X1,nil),nil) != esk48_0
| ~ ssItem(esk52_3(X1,nil,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_18])]) ).
cnf(c_0_37,negated_conjecture,
( ssItem(esk52_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk48_0
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_18])]) ).
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,
( singletonP(esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_41,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_42,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_43,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_44,negated_conjecture,
( app(cons(X1,nil),nil) != esk48_0
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_18])]),c_0_32]) ).
cnf(c_0_45,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_46,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_47,negated_conjecture,
( singletonP(esk48_0)
| ~ neq(esk51_0,nil) ),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_50,plain,
! [X400,X401] :
( ~ ssList(X400)
| ~ ssList(X401)
| ~ segmentP(X400,X401)
| ~ segmentP(X401,X400)
| X400 = X401 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).
cnf(c_0_51,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_52,negated_conjecture,
( cons(X1,nil) != esk48_0
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_18])]) ).
cnf(c_0_53,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_55,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( esk51_0 = nil
| singletonP(esk48_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_18]),c_0_49])]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,negated_conjecture,
segmentP(esk51_0,esk48_0),
inference(rw,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_59,negated_conjecture,
( ~ singletonP(esk48_0)
| ~ ssItem(esk5_1(esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53])]),c_0_54])]) ).
cnf(c_0_60,negated_conjecture,
( esk51_0 = nil
| ssItem(esk5_1(esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_54])]) ).
cnf(c_0_61,negated_conjecture,
( esk51_0 = esk48_0
| ~ segmentP(esk48_0,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_49]),c_0_54])]) ).
cnf(c_0_62,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_64,plain,
! [X407] :
( ~ ssList(X407)
| segmentP(X407,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_65,negated_conjecture,
~ segmentP(esk48_0,nil),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_62]),c_0_63]) ).
cnf(c_0_66,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC229+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
% 0.15/0.32 % Computer : n009.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 04:36:56 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 3.07/2.96 % Version : CSE_E---1.7
% 3.07/2.96 % Problem : theBenchmark.p
% 3.07/2.96 % SZS status Theorem for theBenchmark.p
% 3.07/2.96 % SZS output start CNFRefutation
% See solution above
% 3.07/2.97 % Total time : 2.383s
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