%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC046+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 : n018.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 05:18:02 PM UTC 2026
% Result : Theorem 1.43s 1.75s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 140 ( 35 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 172 ( 65 ~; 62 |; 23 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X4,X5) )
| ( memberP(X3,X5)
& ( ~ memberP(X4,X5)
| ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X4,X5) )
| ( memberP(X3,X5)
& ( ~ memberP(X4,X5)
| ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_7,negated_conjecture,
! [X465,X467] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& nil = esk49_0
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssList(esk52_1(X465))
| memberP(esk50_0,X465)
| ~ memberP(esk51_0,X465)
| ~ ssItem(X465) )
& ( segmentP(esk51_0,app(app(cons(X465,nil),esk52_1(X465)),cons(X465,nil)))
| memberP(esk50_0,X465)
| ~ memberP(esk51_0,X465)
| ~ ssItem(X465) )
& ( memberP(esk51_0,X465)
| ~ memberP(esk50_0,X465)
| ~ ssItem(X465) )
& ( ~ ssList(X467)
| ~ segmentP(esk51_0,app(app(cons(X465,nil),X467),cons(X465,nil)))
| ~ memberP(esk50_0,X465)
| ~ ssItem(X465) ) ),
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_8,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_9,plain,
! [X364,X365,X366] :
( ( ~ memberP(cons(X365,X366),X364)
| X364 = X365
| memberP(X366,X364)
| ~ ssList(X366)
| ~ ssItem(X365)
| ~ ssItem(X364) )
& ( X364 != X365
| memberP(cons(X365,X366),X364)
| ~ ssList(X366)
| ~ ssItem(X365)
| ~ ssItem(X364) )
& ( ~ memberP(X366,X364)
| memberP(cons(X365,X366),X364)
| ~ ssList(X366)
| ~ ssItem(X365)
| ~ ssItem(X364) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_10,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
nil = esk49_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X367] :
( ~ ssItem(X367)
| ~ memberP(nil,X367) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
cnf(c_0_13,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X423] :
( ~ ssList(X423)
| nil = X423
| cons(hd(X423),tl(X423)) = X423 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_15,plain,
! [X334] :
( ~ ssList(X334)
| nil = X334
| ssItem(hd(X334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
fof(c_0_16,plain,
! [X337] :
( ~ ssList(X337)
| nil = X337
| ssList(tl(X337)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_17,negated_conjecture,
( memberP(esk51_0,X1)
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
esk51_0 = nil,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_19,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_28,plain,
( nil = X1
| memberP(X1,hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
esk50_0 != nil,
inference(rw,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
~ ssItem(hd(esk50_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC046+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 04:19:47 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.43/1.75 % Version : CSE_E---1.7
% 1.43/1.75 % Problem : theBenchmark.p
% 1.43/1.75 % SZS status Theorem for theBenchmark.p
% 1.43/1.75 % SZS output start CNFRefutation
% See solution above
% 1.43/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------