%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC384+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 : n005.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 05:19:26 PM UTC 2026
% Result : Theorem 1.37s 1.74s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 204 ( 61 equ)
% Maximal formula atoms : 45 ( 4 avg)
% Number of connectives : 244 ( 84 ~; 96 |; 42 &)
% ( 3 <=>; 19 =>; 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 : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 29 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X5,nil) != X3
| app(app(X6,X3),X7) != X4
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( singletonP(X1)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X5,nil) != X3
| app(app(X6,X3),X7) != X4
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( singletonP(X1)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_7,plain,
! [X243,X244,X247,X248] :
( ( ssList(esk8_2(X243,X244))
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( ssList(esk9_2(X243,X244))
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( app(app(esk8_2(X243,X244),X244),esk9_2(X243,X244)) = X243
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( ~ ssList(X247)
| ~ ssList(X248)
| app(app(X247,X244),X248) != X243
| segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
fof(c_0_8,negated_conjecture,
! [X473,X474] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ( nil = esk51_0
| ssItem(esk52_0) )
& ( nil = esk50_0
| ssItem(esk52_0) )
& ( nil = esk51_0
| ssList(esk53_0) )
& ( nil = esk50_0
| ssList(esk53_0) )
& ( nil = esk51_0
| ssList(esk54_0) )
& ( nil = esk50_0
| ssList(esk54_0) )
& ( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk51_0
| app(app(esk53_0,esk50_0),esk54_0) = esk51_0 )
& ( nil = esk50_0
| app(app(esk53_0,esk50_0),esk54_0) = esk51_0 )
& ( nil = esk51_0
| ~ ssItem(X473)
| ~ memberP(esk53_0,X473)
| ~ lt(esk52_0,X473) )
& ( nil = esk50_0
| ~ ssItem(X473)
| ~ memberP(esk53_0,X473)
| ~ lt(esk52_0,X473) )
& ( nil = esk51_0
| ~ ssItem(X474)
| ~ memberP(esk54_0,X474)
| ~ lt(X474,esk52_0) )
& ( nil = esk50_0
| ~ ssItem(X474)
| ~ memberP(esk54_0,X474)
| ~ lt(X474,esk52_0) )
& ( ~ singletonP(esk48_0)
| ~ segmentP(esk49_0,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_9,plain,
! [X232,X234] :
( ( ssItem(esk5_1(X232))
| ~ singletonP(X232)
| ~ ssList(X232) )
& ( cons(esk5_1(X232),nil) = X232
| ~ singletonP(X232)
| ~ ssList(X232) )
& ( ~ ssItem(X234)
| cons(X234,nil) != X232
| singletonP(X232)
| ~ ssList(X232) ) ),
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_10,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_7]) ).
cnf(c_0_11,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( ~ singletonP(esk48_0)
| ~ segmentP(esk49_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,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_10]) ).
cnf(c_0_18,negated_conjecture,
( nil = esk50_0
| app(app(esk53_0,esk50_0),esk54_0) = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( nil = esk50_0
| ssList(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( nil = esk50_0
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( nil = esk50_0
| cons(esk52_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
( nil = esk50_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( nil = esk51_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ singletonP(esk50_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_12]),c_0_14]) ).
cnf(c_0_29,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,esk50_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),c_0_21]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( esk50_0 = nil
| singletonP(esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]),c_0_25]) ).
fof(c_0_31,plain,
~ singletonP(nil),
inference(fof_simplification,[status(thm)],[ax39]) ).
fof(c_0_32,plain,
! [X324,X325] :
( ( ~ neq(X324,X325)
| X324 != X325
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X324 = X325
| neq(X324,X325)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_33,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,negated_conjecture,
( esk51_0 = nil
| singletonP(esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_26]),c_0_20])]),c_0_27]) ).
cnf(c_0_35,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_36,plain,
~ singletonP(nil),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_33,c_0_12]) ).
cnf(c_0_39,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC384+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
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:47:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.37/1.74 % Version : CSE_E---1.7
% 1.37/1.74 % Problem : theBenchmark.p
% 1.37/1.74 % SZS status Theorem for theBenchmark.p
% 1.37/1.74 % SZS output start CNFRefutation
% See solution above
% 1.37/1.75 % Total time : 1.368s
%------------------------------------------------------------------------------