%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC198+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 : n012.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 05:18:41 PM UTC 2026
% Result : Theorem 1.46s 1.69s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 142 ( 45 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 175 ( 61 ~; 64 |; 32 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) )
| ( ! [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/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(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax2,axiom,
? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) )
| ( ! [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_6,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_7,plain,
! [X367,X368,X369] :
( ( ~ memberP(cons(X368,X369),X367)
| X367 = X368
| memberP(X369,X367)
| ~ ssList(X369)
| ~ ssItem(X368)
| ~ ssItem(X367) )
& ( X367 != X368
| memberP(cons(X368,X369),X367)
| ~ ssList(X369)
| ~ ssItem(X368)
| ~ ssItem(X367) )
& ( ~ memberP(X369,X367)
| memberP(cons(X368,X369),X367)
| ~ ssList(X369)
| ~ ssItem(X368)
| ~ ssItem(X367) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(c_0_8,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) )
& ( memberP(esk48_0,esk52_1(X468))
| ~ ssItem(X468) )
& ( X468 != esk52_1(X468)
| ~ ssItem(X468) )
& ( 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_5])])])])]) ).
fof(c_0_9,plain,
! [X370] :
( ~ ssItem(X370)
| ~ memberP(nil,X370) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_10,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_13,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( memberP(esk48_0,esk52_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( esk50_0 = nil
| esk53_0 = X1
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]),c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( memberP(esk50_0,esk52_1(X1))
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ssItem(esk52_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( X1 != esk52_1(X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( esk52_1(X1) = esk53_0
| esk50_0 = nil
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]),c_0_13]) ).
fof(c_0_23,plain,
( ssItem(esk1_0)
& ssItem(esk2_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[ax2])]) ).
cnf(c_0_24,negated_conjecture,
( memberP(nil,esk52_1(X1))
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_25,plain,
ssItem(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ ssItem(X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_24]),c_0_19]) ).
cnf(c_0_27,plain,
$false,
inference(sr,[status(thm)],[c_0_25,c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC198+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.06 % 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
% 0.07/0.25 % Computer : n012.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 : Tue May 5 04:32:46 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 1.46/1.69 % Version : CSE_E---1.7
% 1.46/1.69 % Problem : theBenchmark.p
% 1.46/1.69 % SZS status Theorem for theBenchmark.p
% 1.46/1.69 % SZS output start CNFRefutation
% See solution above
% 1.46/1.69 % Total time : 1.364s
%------------------------------------------------------------------------------