%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC098+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 : n024.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 05:18:16 PM UTC 2026
% Result : Theorem 1.08s 1.62s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 171 ( 73 equ)
% Maximal formula atoms : 46 ( 4 avg)
% Number of connectives : 220 ( 85 ~; 87 |; 34 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X2,X6)
| ~ leq(X5,X6)
| X5 = X6 ) )
& memberP(X2,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [X7] :
( ssItem(X7)
=> ( cons(X7,nil) != X3
| ~ memberP(X4,X7)
| ? [X8] :
( ssItem(X8)
& X7 != X8
& memberP(X4,X8)
& leq(X7,X8) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X2,X6)
| ~ leq(X5,X6)
| X5 = X6 ) )
& memberP(X2,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [X7] :
( ssItem(X7)
=> ( cons(X7,nil) != X3
| ~ memberP(X4,X7)
| ? [X8] :
( ssItem(X8)
& X7 != X8
& memberP(X4,X8)
& leq(X7,X8) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_4,negated_conjecture,
! [X468,X471] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ssItem(esk52_1(X468))
| ~ ssItem(X468)
| cons(X468,nil) != esk48_0
| ~ memberP(esk49_0,X468) )
& ( memberP(esk49_0,esk52_1(X468))
| ~ ssItem(X468)
| cons(X468,nil) != esk48_0
| ~ memberP(esk49_0,X468) )
& ( leq(X468,esk52_1(X468))
| ~ ssItem(X468)
| cons(X468,nil) != esk48_0
| ~ memberP(esk49_0,X468) )
& ( X468 != esk52_1(X468)
| ~ ssItem(X468)
| cons(X468,nil) != esk48_0
| ~ memberP(esk49_0,X468) )
& ( nil != esk49_0
| nil != esk48_0 )
& ( nil = esk51_0
| ssItem(esk53_0) )
& ( nil = esk50_0
| ssItem(esk53_0) )
& ( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk51_0
| ~ ssItem(X471)
| esk53_0 = X471
| ~ memberP(esk51_0,X471)
| ~ leq(esk53_0,X471) )
& ( nil = esk50_0
| ~ ssItem(X471)
| esk53_0 = X471
| ~ memberP(esk51_0,X471)
| ~ leq(esk53_0,X471) ) ),
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_3])])])])]) ).
fof(c_0_5,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| cons(X327,X326) != X326 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_6,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_12,negated_conjecture,
( nil = esk51_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( leq(X1,esk52_1(X1))
| ~ ssItem(X1)
| cons(X1,nil) != esk48_0
| ~ memberP(esk49_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
esk50_0 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),c_0_12]),c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( nil = esk50_0
| memberP(esk51_0,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,negated_conjecture,
( memberP(esk49_0,esk52_1(X1))
| ~ ssItem(X1)
| cons(X1,nil) != esk48_0
| ~ memberP(esk49_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,negated_conjecture,
( ssItem(esk52_1(X1))
| ~ ssItem(X1)
| cons(X1,nil) != esk48_0
| ~ memberP(esk49_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_21,negated_conjecture,
( X1 != esk52_1(X1)
| ~ ssItem(X1)
| cons(X1,nil) != esk48_0
| ~ memberP(esk49_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,negated_conjecture,
( nil = esk50_0
| esk53_0 = X1
| ~ ssItem(X1)
| ~ memberP(esk51_0,X1)
| ~ leq(esk53_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,negated_conjecture,
( leq(X1,esk52_1(X1))
| cons(X1,nil) != esk50_0
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_7]),c_0_8]) ).
cnf(c_0_24,negated_conjecture,
cons(esk53_0,nil) = esk50_0,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
memberP(esk51_0,esk53_0),
inference(sr,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_27,negated_conjecture,
( memberP(esk51_0,esk52_1(X1))
| cons(X1,nil) != esk50_0
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_8]),c_0_7]),c_0_8]) ).
cnf(c_0_28,negated_conjecture,
( ssItem(esk52_1(X1))
| cons(X1,nil) != esk50_0
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_7]),c_0_8]) ).
cnf(c_0_29,negated_conjecture,
( cons(X1,nil) != esk50_0
| esk52_1(X1) != X1
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_7]),c_0_8]) ).
cnf(c_0_30,negated_conjecture,
( esk53_0 = X1
| ~ leq(esk53_0,X1)
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(sr,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_31,negated_conjecture,
leq(esk53_0,esk52_1(esk53_0)),
inference(cn,[status(thm)],[inference(rw,[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_32,negated_conjecture,
memberP(esk51_0,esk52_1(esk53_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_33,negated_conjecture,
ssItem(esk52_1(esk53_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_34,negated_conjecture,
esk52_1(esk53_0) != esk53_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC098+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.06 % 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
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Mon May 4 23:25:26 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.08/1.62 % Version : CSE_E---1.7
% 1.08/1.62 % Problem : theBenchmark.p
% 1.08/1.62 % SZS status Theorem for theBenchmark.p
% 1.08/1.62 % SZS output start CNFRefutation
% See solution above
% 1.08/1.62 % Total time : 1.362s
%------------------------------------------------------------------------------