%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC233+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 05:18:49 PM UTC 2026
% Result : Theorem 3.64s 3.10s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 7 unt; 0 def)
% Number of atoms : 241 ( 62 equ)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 322 ( 129 ~; 125 |; 42 &)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 46 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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
| 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)
| lt(X5,X8) ) ) ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& app(app(X10,cons(X9,nil)),X11) = X3
& ? [X12] :
( ssItem(X12)
& ( ( ~ lt(X9,X12)
& memberP(X11,X12) )
| ( ~ lt(X12,X9)
& memberP(X10,X12) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(c_0_10,plain,
! [X446,X447] :
( ( nil = X447
| nil != app(X446,X447)
| ~ ssList(X447)
| ~ ssList(X446) )
& ( nil = X446
| nil != app(X446,X447)
| ~ ssList(X447)
| ~ ssList(X446) )
& ( nil != X447
| nil != X446
| nil = app(X446,X447)
| ~ ssList(X447)
| ~ ssList(X446) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_11,plain,
! [X332,X333] :
( ~ ssList(X332)
| ~ ssItem(X333)
| ssList(cons(X333,X332)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_12,plain,
! [X353,X354,X355] :
( ~ ssList(X353)
| ~ ssList(X354)
| ~ ssItem(X355)
| cons(X355,app(X354,X353)) = app(cons(X355,X354),X353) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_13,plain,
! [X351,X352] :
( ~ ssList(X351)
| ~ ssList(X352)
| ssList(app(X351,X352)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_14,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != 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)
| lt(X5,X8) ) ) ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& app(app(X10,cons(X9,nil)),X11) = X3
& ? [X12] :
( ssItem(X12)
& ( ( ~ lt(X9,X12)
& memberP(X11,X12) )
| ( ~ lt(X12,X9)
& memberP(X10,X12) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_17,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]),c_0_15])]) ).
fof(c_0_21,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_22,negated_conjecture,
! [X476,X477,X478,X480,X481,X482,X483] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( memberP(X477,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( memberP(X478,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( leq(X476,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ lt(X476,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( lt(X480,X483)
| ~ memberP(X482,X483)
| ~ ssItem(X483)
| ~ ssList(X482)
| app(app(X481,cons(X480,nil)),X482) != esk50_0
| ~ ssList(X481)
| ~ ssItem(X480) )
& ( lt(X483,X480)
| ~ memberP(X481,X483)
| ~ ssItem(X483)
| ~ ssList(X482)
| app(app(X481,cons(X480,nil)),X482) != esk50_0
| ~ ssList(X481)
| ~ ssItem(X480) ) ),
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_16])])])])]) ).
fof(c_0_23,plain,
! [X356] :
( ~ ssList(X356)
| app(nil,X356) = X356 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_24,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,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_18,c_0_20]),c_0_15])]) ).
fof(c_0_26,plain,
! [X378] :
( ~ ssItem(X378)
| ~ memberP(nil,X378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
cnf(c_0_27,negated_conjecture,
( memberP(X1,esk52_3(X2,X1,X3))
| ~ ssList(X3)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15])]) ).
cnf(c_0_30,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( memberP(nil,esk52_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_15])]),c_0_29]) ).
cnf(c_0_32,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_22]) ).
cnf(c_0_33,negated_conjecture,
( app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(esk52_3(X1,nil,X2))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,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_32,c_0_28]),c_0_15])]) ).
fof(c_0_35,plain,
! [X441,X442] :
( ~ ssList(X441)
| ~ ssItem(X442)
| cons(X442,X441) = app(cons(X442,nil),X441) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_36,negated_conjecture,
( app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]) ).
cnf(c_0_37,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_38,plain,
! [X340] :
( ( ssList(esk44_1(X340))
| nil = X340
| ~ ssList(X340) )
& ( ssItem(esk45_1(X340))
| nil = X340
| ~ ssList(X340) )
& ( cons(esk45_1(X340),esk44_1(X340)) = X340
| nil = X340
| ~ ssList(X340) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_39,negated_conjecture,
( cons(X1,X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(esk44_1(esk48_0))
| ~ ssItem(esk45_1(esk48_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40])]),c_0_41])]),c_0_42]) ).
cnf(c_0_44,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
~ ssItem(esk45_1(esk48_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_41])]),c_0_42]) ).
cnf(c_0_46,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC233+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n004.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 04:36:32 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 3.64/3.10 % Version : CSE_E---1.7
% 3.64/3.10 % Problem : theBenchmark.p
% 3.64/3.10 % SZS status Theorem for theBenchmark.p
% 3.64/3.10 % SZS output start CNFRefutation
% See solution above
% 3.64/3.11 % Total time : 2.373s
%------------------------------------------------------------------------------