%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL469+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 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 : n031.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 04:40:27 PM UTC 2026
% Result : Theorem 0.31s 1.62s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 43 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 10 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(cn2,axiom,
( cn2
<=> ! [X4,X5] : is_a_theorem(implies(X4,implies(not(X4),X5))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn2) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(hilbert_or_1,conjecture,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(luka_cn2,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
fof(luka_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_op_or) ).
fof(c_0_8,plain,
! [X186,X187] :
( ~ op_implies_and
| implies(X186,X187) = not(and(X186,not(X187))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
fof(c_0_9,plain,
! [X154,X155] :
( ( ~ cn2
| is_a_theorem(implies(X154,implies(not(X154),X155))) )
& ( ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))
| cn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])]) ).
fof(c_0_10,plain,
! [X182,X183] :
( ~ op_or
| or(X182,X183) = not(and(not(X182),not(X183))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_11,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_13,plain,
! [X110,X111] :
( ( ~ or_1
| is_a_theorem(implies(X110,or(X110,X111))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).
fof(c_0_14,negated_conjecture,
~ or_1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_or_1])]) ).
cnf(c_0_15,plain,
( is_a_theorem(implies(X1,implies(not(X1),X2)))
| ~ cn2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
cn2,
inference(split_conjunct,[status(thm)],[luka_cn2]) ).
cnf(c_0_17,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_19,plain,
op_or,
inference(split_conjunct,[status(thm)],[luka_op_or]) ).
cnf(c_0_20,plain,
( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
~ or_1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_23,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_24,plain,
~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))),
inference(sr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL469+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 22:39:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.31/1.62 % Version : CSE_E---1.7
% 0.31/1.62 % Problem : theBenchmark.p
% 0.31/1.62 % SZS status Theorem for theBenchmark.p
% 0.31/1.62 % SZS output start CNFRefutation
% See solution above
% 0.31/1.62 % Total time : 1.272s
%------------------------------------------------------------------------------