%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC243+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 : n001.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 05:18:52 PM UTC 2026
% Result : Theorem 2.44s 2.03s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 7 unt; 0 def)
% Number of atoms : 207 ( 57 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 270 ( 110 ~; 107 |; 27 &)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 42 !; 8 ?)
% 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
| ~ totalorderedP(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)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) ) ) ) ) ) ),
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,
! [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_11,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_12,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_13,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_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
| ~ totalorderedP(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)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) ) ) ) ) ) ),
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,
! [X468,X469,X470] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& totalorderedP(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) )
& ( lt(X468,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) ) ),
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,
! [X348] :
( ~ ssList(X348)
| app(nil,X348) = X348 ),
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,
! [X370] :
( ~ ssItem(X370)
| ~ memberP(nil,X370) ),
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,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_31,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,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_33,negated_conjecture,
( ssItem(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_30,c_0_28]),c_0_15])]),c_0_29]) ).
fof(c_0_34,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_35,negated_conjecture,
( app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_36,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_37,plain,
! [X332] :
( ( ssList(esk44_1(X332))
| nil = X332
| ~ ssList(X332) )
& ( ssItem(esk45_1(X332))
| nil = X332
| ~ ssList(X332) )
& ( cons(esk45_1(X332),esk44_1(X332)) = X332
| nil = X332
| ~ ssList(X332) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_38,negated_conjecture,
( cons(X1,X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_41,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,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_38,c_0_39])]),c_0_40])]),c_0_41]) ).
cnf(c_0_43,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,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_42,c_0_43]),c_0_40])]),c_0_41]) ).
cnf(c_0_45,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC243+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
% 0.15/0.33 % Computer : n001.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 04:40:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.44/2.03 % Version : CSE_E---1.7
% 2.44/2.03 % Problem : theBenchmark.p
% 2.44/2.03 % SZS status Theorem for theBenchmark.p
% 2.44/2.03 % SZS output start CNFRefutation
% See solution above
% 2.44/2.04 % Total time : 1.374s
%------------------------------------------------------------------------------