%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:13:01 PM UTC 2026
% Result : Theorem 0.90s 0.62s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 28
% Syntax : Number of formulae : 139 ( 75 unt; 0 def)
% Number of atoms : 265 ( 51 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 208 ( 82 ~; 87 |; 20 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 193 ( 12 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X2)
& is_a_theorem(X1) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X1,X2] : strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
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(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
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(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(strict_implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(hilbert_modus_ponens,conjecture,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(s1_0_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_equiv) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(c_0_28,plain,
! [X133,X134] :
( ( adjunction
| ~ is_a_theorem(and(esk59_0,esk60_0)) )
& ( adjunction
| is_a_theorem(esk60_0) )
& ( adjunction
| is_a_theorem(esk59_0) )
& ( is_a_theorem(and(X133,X134))
| ~ is_a_theorem(X134)
| ~ is_a_theorem(X133)
| ~ adjunction ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])])]) ).
fof(c_0_29,plain,
! [X209,X210] :
( strict_equiv(X209,X210) = and(strict_implies(X209,X210),strict_implies(X210,X209))
| ~ op_strict_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ adjunction
| is_a_theorem(and(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_32,plain,
( ~ op_strict_equiv
| strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
fof(c_0_34,plain,
! [X169,X170] :
( ( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))) )
& ( is_a_theorem(strict_implies(and(X169,X170),and(X170,X169)))
| ~ axiom_m1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])]) ).
fof(c_0_35,plain,
! [X137,X138] :
( ( substitution_strict_equiv
| esk61_0 != esk62_0 )
& ( substitution_strict_equiv
| is_a_theorem(strict_equiv(esk61_0,esk62_0)) )
& ( X137 = X138
| ~ is_a_theorem(strict_equiv(X137,X138))
| ~ substitution_strict_equiv ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])])]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_37,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_38,plain,
( ~ axiom_m1
| is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
fof(c_0_40,plain,
! [X121,X122] :
( implies(X121,X122) = not(and(X121,not(X122)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| ~ substitution_strict_equiv
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_43,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(strict_equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
fof(c_0_45,plain,
! [X207,X208] :
( strict_implies(X207,X208) = necessarily(implies(X207,X208))
| ~ op_strict_implies ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])]) ).
fof(c_0_46,plain,
! [X117,X118] :
( or(X117,X118) = not(and(not(X117),not(X118)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_47,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_50,plain,
is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_44])]) ).
cnf(c_0_51,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_53,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_55,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_56,plain,
and(X1,X2) = and(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_57,plain,
! [X183] :
( ( axiom_m4
| ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0))) )
& ( is_a_theorem(strict_implies(X183,and(X183,X183)))
| ~ axiom_m4 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])]) ).
fof(c_0_58,plain,
! [X173,X174] :
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)) )
& ( is_a_theorem(strict_implies(and(X173,X174),X173))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])]) ).
fof(c_0_59,plain,
! [X129,X130] :
( ( modus_ponens_strict_implies
| ~ is_a_theorem(esk58_0) )
& ( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk57_0,esk58_0)) )
& ( modus_ponens_strict_implies
| is_a_theorem(esk57_0) )
& ( is_a_theorem(X130)
| ~ is_a_theorem(strict_implies(X129,X130))
| ~ is_a_theorem(X129)
| ~ modus_ponens_strict_implies ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies])])])])])]) ).
fof(c_0_60,plain,
! [X185,X186,X187] :
( ( axiom_m5
| ~ is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0))) )
& ( is_a_theorem(strict_implies(and(strict_implies(X185,X186),strict_implies(X186,X187)),strict_implies(X185,X187)))
| ~ axiom_m5 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])])]) ).
cnf(c_0_61,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_62,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_63,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_54,c_0_56]) ).
cnf(c_0_64,plain,
( ~ axiom_m4
| is_a_theorem(strict_implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_66,plain,
( ~ axiom_m2
| is_a_theorem(strict_implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_70,plain,
( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
cnf(c_0_72,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_73,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_63]),c_0_62]),c_0_62]) ).
cnf(c_0_74,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_75,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_77,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
cnf(c_0_78,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_72]) ).
cnf(c_0_79,plain,
is_a_theorem(strict_equiv(and(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_74]),c_0_75])]) ).
cnf(c_0_80,plain,
( ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
strict_implies(not(X1),and(not(X2),X3)) = strict_implies(implies(X3,X2),X1),
inference(spm,[status(thm)],[c_0_78,c_0_63]) ).
cnf(c_0_82,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_54,c_0_54]) ).
cnf(c_0_83,plain,
and(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_79]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(strict_implies(X1,X3))
| ~ is_a_theorem(strict_implies(X3,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_80,c_0_36]) ).
cnf(c_0_85,plain,
is_a_theorem(strict_implies(or(X1,X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_81]),c_0_62]) ).
cnf(c_0_86,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_62,c_0_54]) ).
cnf(c_0_87,plain,
implies(implies(X1,X2),and(X1,not(X2))) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(strict_implies(X1,and(X2,X3)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_75]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),and(X1,not(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(strict_implies(X1,or(X2,X2)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_83]),c_0_62]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_78]) ).
cnf(c_0_93,plain,
is_a_theorem(strict_implies(not(X1),not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_85]),c_0_91]),c_0_78]) ).
cnf(c_0_94,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_92,c_0_62]) ).
cnf(c_0_95,plain,
strict_equiv(X1,X2) = strict_equiv(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_56]),c_0_37]) ).
cnf(c_0_96,plain,
is_a_theorem(strict_equiv(not(X1),not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_93]),c_0_78]),c_0_94])]),c_0_95]) ).
cnf(c_0_97,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_75,c_0_56]) ).
cnf(c_0_98,plain,
not(or(X1,X1)) = not(X1),
inference(spm,[status(thm)],[c_0_49,c_0_96]) ).
fof(c_0_99,plain,
! [X11,X12] :
( ( substitution_of_equivalents
| esk3_0 != esk4_0 )
& ( substitution_of_equivalents
| is_a_theorem(equiv(esk3_0,esk4_0)) )
& ( X11 = X12
| ~ is_a_theorem(equiv(X11,X12))
| ~ substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])]) ).
fof(c_0_100,plain,
! [X125,X126] :
( equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
fof(c_0_101,negated_conjecture,
~ modus_ponens,
inference(assume_negation,[status(cth)],[hilbert_modus_ponens]) ).
cnf(c_0_102,plain,
( ~ is_a_theorem(strict_implies(X1,and(X3,X2)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_97]) ).
cnf(c_0_103,plain,
implies(X1,or(X2,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_98]),c_0_54]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_105,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_106,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_equiv]) ).
fof(c_0_108,negated_conjecture,
~ modus_ponens,
inference(fof_simplification,[status(thm)],[c_0_101]) ).
cnf(c_0_109,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_102,c_0_89]) ).
cnf(c_0_110,plain,
is_a_theorem(strict_implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_62]),c_0_81]),c_0_62]) ).
cnf(c_0_111,plain,
strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_103]),c_0_61]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_113,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
fof(c_0_114,plain,
! [X7,X8] :
( ( modus_ponens
| ~ is_a_theorem(esk2_0) )
& ( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) )
& ( modus_ponens
| is_a_theorem(esk1_0) )
& ( is_a_theorem(X8)
| ~ is_a_theorem(implies(X7,X8))
| ~ is_a_theorem(X7)
| ~ modus_ponens ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_115,negated_conjecture,
~ modus_ponens,
inference(fof_nnf,[status(thm)],[c_0_108]) ).
cnf(c_0_116,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_109,c_0_78]) ).
cnf(c_0_117,plain,
is_a_theorem(strict_implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_110,c_0_91]) ).
cnf(c_0_118,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_76,c_0_111]) ).
cnf(c_0_119,plain,
( ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1)))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_120,plain,
( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_121,negated_conjecture,
~ modus_ponens,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(not(not(X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_116]) ).
cnf(c_0_123,plain,
not(not(not(X1))) = not(X1),
inference(spm,[status(thm)],[c_0_98,c_0_91]) ).
cnf(c_0_124,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_76,c_0_117]) ).
cnf(c_0_125,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(X1,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_74]),c_0_83]),c_0_83]) ).
cnf(c_0_126,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_119,c_0_36]) ).
cnf(c_0_127,plain,
is_a_theorem(implies(esk1_0,esk2_0)),
inference(sr,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_128,plain,
( ~ is_a_theorem(not(X2))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_129,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_130,plain,
implies(X1,not(not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_123]),c_0_54]) ).
cnf(c_0_131,plain,
( modus_ponens
| is_a_theorem(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_132,plain,
( ~ is_a_theorem(esk2_0)
| modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_133,plain,
( ~ is_a_theorem(implies(esk2_0,esk1_0))
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_134,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_135,plain,
is_a_theorem(esk1_0),
inference(sr,[status(thm)],[c_0_131,c_0_121]) ).
cnf(c_0_136,plain,
~ is_a_theorem(esk2_0),
inference(sr,[status(thm)],[c_0_132,c_0_121]) ).
cnf(c_0_137,plain,
esk2_0 = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135])]) ).
cnf(c_0_138,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137]),c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 00:39:02 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.90/0.62 % Version: 3.5.1
% 0.90/0.62 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.90/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.62 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.90/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.90/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.90/0.62 % Starting sh5l with 300s (1) cores
% 0.90/0.62 % new_bool_1 with pid 1619366 completed with status 9
% 0.90/0.62 % sh5l with pid 1619367 completed with status 9
% 0.90/0.62 % new_bool_3 with pid 1619365 completed with status 9
% 0.90/0.62 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1619364 completed with status 0
% 0.90/0.62 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.90/0.62 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.90/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.62 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.90/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.90/0.62 % No SInE strategy applied
% 0.90/0.62 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.90/0.62 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.90/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.90/0.62 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.90/0.62 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 0.90/0.62 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.90/0.62 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.90/0.62 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1619370 completed with status 0
% 0.90/0.62 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.90/0.62 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.90/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.62 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.90/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.90/0.62 % No SInE strategy applied
% 0.90/0.62 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.90/0.62 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.90/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.90/0.62 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.90/0.62 % Preprocessing time : 0.002 s
% 0.90/0.62 % Presaturation interreduction done
% 0.90/0.62
% 0.90/0.62 % Proof found!
% 0.90/0.62 % SZS status Theorem
% 0.90/0.62 % SZS output start CNFRefutation
% See solution above
% 0.90/0.62 % Parsed axioms : 77
% 0.90/0.62 % Removed by relevancy pruning/SinE : 0
% 0.90/0.62 % Initial clauses : 135
% 0.90/0.62 % Removed in clause preprocessing : 0
% 0.90/0.62 % Initial clauses in saturation : 135
% 0.90/0.62 % Processed clauses : 1080
% 0.90/0.62 % ...of these trivial : 241
% 0.90/0.62 % ...subsumed : 313
% 0.90/0.62 % ...remaining for further processing : 526
% 0.90/0.62 % Other redundant clauses eliminated : 0
% 0.90/0.62 % Clauses deleted for lack of memory : 0
% 0.90/0.62 % Backward-subsumed : 10
% 0.90/0.62 % Backward-rewritten : 27
% 0.90/0.62 % Generated clauses : 10221
% 0.90/0.62 % ...of the previous two non-redundant : 7916
% 0.90/0.62 % ...aggressively subsumed : 0
% 0.90/0.62 % Contextual simplify-reflections : 0
% 0.90/0.62 % Paramodulations : 10221
% 0.90/0.62 % Factorizations : 0
% 0.90/0.62 % NegExts : 0
% 0.90/0.62 % Equation resolutions : 0
% 0.90/0.62 % Disequality decompositions : 0
% 0.90/0.62 % Total rewrite steps : 9832
% 0.90/0.62 % ...of those cached : 8025
% 0.90/0.62 % Propositional unsat checks : 0
% 0.90/0.62 % Propositional check models : 0
% 0.90/0.63 % Propositional check unsatisfiable : 0
% 0.90/0.63 % Propositional clauses : 0
% 0.90/0.63 % Propositional clauses after purity: 0
% 0.90/0.63 % Propositional unsat core size : 0
% 0.90/0.63 % Propositional preprocessing time : 0.000
% 0.90/0.63 % Propositional encoding time : 0.000
% 0.90/0.63 % Propositional solver time : 0.000
% 0.90/0.63 % Success case prop preproc time : 0.000
% 0.90/0.63 % Success case prop encoding time : 0.000
% 0.90/0.63 % Success case prop solver time : 0.000
% 0.90/0.63 % Current number of processed clauses : 372
% 0.90/0.63 % Positive orientable unit clauses : 190
% 0.90/0.63 % Positive unorientable unit clauses: 13
% 0.90/0.63 % Negative unit clauses : 1
% 0.90/0.63 % Non-unit-clauses : 168
% 0.90/0.63 % Current number of unprocessed clauses: 7060
% 0.90/0.63 % ...number of literals in the above : 9239
% 0.90/0.63 % Current number of archived formulas : 0
% 0.90/0.63 % Current number of archived clauses : 154
% 0.90/0.63 % Clause-clause subsumption calls (NU) : 3422
% 0.90/0.63 % Rec. Clause-clause subsumption calls : 1989
% 0.90/0.63 % Non-unit clause-clause subsumptions : 276
% 0.90/0.63 % Unit Clause-clause subsumption calls : 648
% 0.90/0.63 % Rewrite failures with RHS unbound : 0
% 0.90/0.63 % BW rewrite match attempts : 384
% 0.90/0.63 % BW rewrite match successes : 113
% 0.90/0.63 % Condensation attempts : 0
% 0.90/0.63 % Condensation successes : 0
% 0.90/0.63 % Termbank termtop insertions : 132668
% 0.90/0.63 % Search garbage collected termcells : 2057
% 0.90/0.63
% 0.90/0.63 % -------------------------------------------------
% 0.90/0.63 % User time : 0.181 s
% 0.90/0.63 % System time : 0.015 s
% 0.90/0.63 % Total time : 0.196 s
% 0.90/0.63 % Maximum resident set size: 3936 pages
% 0.90/0.63
% 0.90/0.63 % -------------------------------------------------
% 0.90/0.63 % User time : 0.870 s
% 0.90/0.63 % System time : 0.112 s
% 0.90/0.63 % Total time : 0.982 s
% 0.90/0.63 % Maximum resident set size: 4608 pages
% 0.90/0.63 % E exiting
%------------------------------------------------------------------------------