%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC009+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 : n002.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 05:17:52 PM UTC 2026
% Result : Theorem 1.35s 1.73s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 99 ( 39 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 117 ( 39 ~; 34 |; 33 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 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 : 41 ( 0 sgn 19 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1 ) ) )
| ! [X8] :
( ssList(X8)
=> ( app(X3,X8) != X4
| ~ strictorderedP(X3)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X8
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(X12,cons(X11,nil)) = X3
& lt(X11,X9) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1 ) ) )
| ! [X8] :
( ssList(X8)
=> ( app(X3,X8) != X4
| ~ strictorderedP(X3)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X8
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(X12,cons(X11,nil)) = X3
& lt(X11,X9) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_4,negated_conjecture,
! [X476,X477,X478,X480,X481,X482,X483] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssList(X476)
| ~ ssList(X477)
| ~ ssList(X478)
| app(app(X476,X477),X478) != esk49_0
| app(X476,X478) != esk48_0 )
& ssList(esk52_0)
& app(esk50_0,esk52_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X480)
| ~ ssList(X481)
| app(cons(X480,nil),X481) != esk52_0
| ~ ssItem(X482)
| ~ ssList(X483)
| app(X483,cons(X482,nil)) != esk50_0
| ~ lt(X482,X480) )
& ( nil = esk51_0
| nil != esk50_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_5,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X1,X2),X3) != esk49_0
| app(X1,X3) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_6,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X448] :
( ~ ssList(X448)
| app(X448,nil) = X448 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_9,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( app(app(X1,X2),X3) != esk51_0
| app(X1,X3) != esk50_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
cnf(c_0_11,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
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,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( app(app(esk50_0,X1),nil) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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])]) ).
cnf(c_0_15,negated_conjecture,
app(esk50_0,esk52_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
app(esk51_0,nil) != esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC009+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n002.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:13:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.35/1.73 % Version : CSE_E---1.7
% 1.35/1.73 % Problem : theBenchmark.p
% 1.35/1.73 % SZS status Theorem for theBenchmark.p
% 1.35/1.73 % SZS output start CNFRefutation
% See solution above
% 1.35/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------