%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC023+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 : 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 05:17:56 PM UTC 2026
% Result : Theorem 1.15s 1.62s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 121 ( 36 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 126 ( 40 ~; 49 |; 24 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ( ! [X6] :
( ssList(X6)
=> ( ~ neq(X6,nil)
| ~ frontsegP(X4,X6)
| ~ frontsegP(X3,X6) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ( ! [X6] :
( ssList(X6)
=> ( ~ neq(X6,nil)
| ~ frontsegP(X4,X6)
| ~ frontsegP(X3,X6) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_5,negated_conjecture,
! [X464] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ( ~ ssList(X464)
| ~ neq(X464,nil)
| ~ frontsegP(esk49_0,X464)
| ~ frontsegP(esk48_0,X464) )
& ( nil = esk51_0
| ssList(esk52_0) )
& ( nil = esk50_0
| ssList(esk52_0) )
& ( nil = esk51_0
| neq(esk52_0,nil) )
& ( nil = esk50_0
| neq(esk52_0,nil) )
& ( nil = esk51_0
| frontsegP(esk51_0,esk52_0) )
& ( nil = esk50_0
| frontsegP(esk51_0,esk52_0) )
& ( nil = esk51_0
| frontsegP(esk50_0,esk52_0) )
& ( nil = esk50_0
| frontsegP(esk50_0,esk52_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_4])])])])]) ).
cnf(c_0_6,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk49_0,X1)
| ~ frontsegP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( ~ frontsegP(esk50_0,X1)
| ~ frontsegP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_10,negated_conjecture,
( nil = esk50_0
| frontsegP(esk50_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( nil = esk50_0
| neq(esk52_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( nil = esk50_0
| ssList(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( nil = esk50_0
| frontsegP(esk51_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,plain,
! [X380] :
( ~ ssList(X380)
| frontsegP(X380,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_16,plain,
! [X381] :
( ( ~ frontsegP(nil,X381)
| nil = X381
| ~ ssList(X381) )
& ( nil != X381
| frontsegP(nil,X381)
| ~ ssList(X381) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
cnf(c_0_17,negated_conjecture,
( nil = esk51_0
| frontsegP(esk50_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_19,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,plain,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( esk51_0 = nil
| frontsegP(nil,esk52_0) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( nil = esk51_0
| ssList(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,negated_conjecture,
( ~ frontsegP(esk51_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_22,c_0_8]) ).
cnf(c_0_28,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_29,negated_conjecture,
( nil = esk51_0
| neq(esk52_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_30,negated_conjecture,
( esk51_0 = nil
| esk52_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_28,c_0_8]) ).
cnf(c_0_33,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC023+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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 23:15:41 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.15/1.62 % Version : CSE_E---1.7
% 1.15/1.62 % Problem : theBenchmark.p
% 1.15/1.62 % SZS status Theorem for theBenchmark.p
% 1.15/1.62 % SZS output start CNFRefutation
% See solution above
% 1.15/1.62 % Total time : 1.363s
%------------------------------------------------------------------------------