%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL488+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 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 : 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 04:40:28 PM UTC 2026
% Result : Theorem 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 30 unt; 0 def)
% Number of atoms : 101 ( 17 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 75 ( 30 ~; 29 |; 7 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 73 ( 6 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(hilbert_and_2,conjecture,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(c_0_16,plain,
! [X162,X163] :
( ( ~ r2
| is_a_theorem(implies(X163,or(X162,X163))) )
& ( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
| r2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])]) ).
fof(c_0_17,plain,
! [X188,X189] :
( ~ op_implies_or
| implies(X188,X189) = or(not(X188),X189) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])]) ).
fof(c_0_18,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_19,plain,
! [X72,X73] :
( ( ~ modus_ponens
| ~ is_a_theorem(X72)
| ~ is_a_theorem(implies(X72,X73))
| is_a_theorem(X73) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])]) ).
fof(c_0_20,plain,
! [X166,X167] :
( ( ~ r3
| is_a_theorem(implies(or(X166,X167),or(X167,X166))) )
& ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])]) ).
cnf(c_0_21,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_23,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_25,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_26,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_28,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_30,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_33,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_34,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_36,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_37,plain,
! [X184,X185] :
( ~ op_and
| and(X184,X185) = not(or(not(X184),not(X185))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])]) ).
cnf(c_0_38,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
fof(c_0_44,plain,
! [X102,X103] :
( ( ~ and_2
| is_a_theorem(implies(and(X102,X103),X103)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])]) ).
fof(c_0_45,negated_conjecture,
~ and_2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_2])]) ).
cnf(c_0_46,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
is_a_theorem(or(X1,implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_33]),c_0_43])]) ).
cnf(c_0_49,plain,
( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
~ and_2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
is_a_theorem(or(implies(X1,not(X2)),X2)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_41,c_0_48]) ).
cnf(c_0_53,plain,
~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL488+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.00/0.12 % 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 : n031.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 : Mon May 4 22:40:38 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.370s
%------------------------------------------------------------------------------