%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL222-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 : Fri Sep 25 02:06:03 PM UTC 2026
% Result : Unsatisfiable 178.22s 36.72s
% Output : CNFRefutation 178.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 172 ( 100 unt; 9 def)
% Number of atoms : 490 ( 10 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 188 ( 99 ~; 89 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 202 ( 0 sgn 202 !; 0 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).
fof(f6,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
fof(f7,axiom,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_2) ).
fof(f9,negated_conjecture,
~ theorem(implies(implies(q,p),implies(or(or(p,q),r),or(p,r)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f10,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f11,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f12,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f13,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f14,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f15,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(or(not(X1),X0))
| theorem(X0) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f16,plain,
~ theorem(or(not(or(not(q),p)),or(not(or(or(p,q),r)),or(p,r)))),
inference(definition_unfolding,[],[f9,f6,f6,f6]) ).
tcf(c_58,plain,
! [X0: $i] : axiom(or(not(or(X0,X0)),X0)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : axiom(or(not(X0),or(X1,X0))),
inference(cnf_transformation,[],[f11]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(cnf_transformation,[],[f12]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(cnf_transformation,[],[f13]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(cnf_transformation,[],[f14]) ).
tcf(c_63,plain,
! [X0: $i] :
( theorem(X0)
| ~ axiom(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( theorem(X1)
| ~ theorem(X0)
| ~ theorem(or(not(X0),X1)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_65,negated_conjecture,
~ theorem(or(not(or(not(q),p)),or(not(or(or(p,q),r)),or(p,r)))),
inference(cnf_transformation,[],[f16]) ).
tcf(c_94,plain,
! [X0: $i] : theorem(or(not(or(X0,X0)),X0)),
inference(resolution,[status(thm)],[c_63,c_58]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] : theorem(or(not(X0),or(X1,X0))),
inference(resolution,[status(thm)],[c_63,c_59]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] : theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(resolution,[status(thm)],[c_63,c_60]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c_63,c_61]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(resolution,[status(thm)],[c_63,c_62]) ).
tcf(c_142,definition,
iPr_def_10 = not(q),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_143,definition,
iPr_def_11 = or(iPr_def_10,p),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_144,definition,
iPr_def_12 = not(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_145,definition,
iPr_def_13 = or(p,q),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_146,definition,
iPr_def_14 = or(iPr_def_13,r),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_147,definition,
iPr_def_15 = not(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_148,definition,
iPr_def_16 = or(p,r),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_149,definition,
iPr_def_17 = or(iPr_def_15,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_150,definition,
iPr_def_18 = or(iPr_def_12,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_151,negated_conjecture,
~ theorem(iPr_def_18),
inference(demodulation,[status(thm)],[c_65,c_148,c_145,c_146,c_147,c_149,c_142,c_143,c_144,c_150]) ).
tcf(c_309,plain,
theorem(or(not(q),iPr_def_13)),
inference(superposition,[status(thm)],[c_145,c_99]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i] :
( theorem(or(X1,X0))
| ~ theorem(X0) ),
inference(superposition,[status(thm)],[c_99,c_64]) ).
tcf(c_316,plain,
theorem(or(iPr_def_10,iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_309,c_142]) ).
tcf(c_346,plain,
theorem(or(not(iPr_def_13),or(q,p))),
inference(superposition,[status(thm)],[c_145,c_104]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_104,c_64]) ).
tcf(c_444,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_10,or(X0,p))),or(X0,iPr_def_11))),
inference(superposition,[status(thm)],[c_143,c_109]) ).
tcf(c_446,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_15,or(X0,iPr_def_16))),or(X0,iPr_def_17))),
inference(superposition,[status(thm)],[c_149,c_109]) ).
tcf(c_447,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_12,or(X0,iPr_def_17))),or(X0,iPr_def_18))),
inference(superposition,[status(thm)],[c_150,c_109]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_109,c_64]) ).
tcf(c_653,plain,
! [X0: $i] : theorem(or(not(or(not(X0),iPr_def_17)),or(not(or(iPr_def_12,X0)),iPr_def_18))),
inference(superposition,[status(thm)],[c_150,c_114]) ).
tcf(c_654,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_114,c_64]) ).
tcf(c_1244,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_11))
| ~ theorem(or(iPr_def_10,or(X0,p))) ),
inference(superposition,[status(thm)],[c_444,c_64]) ).
tcf(c_1260,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_17))
| ~ theorem(or(iPr_def_15,or(X0,iPr_def_16))) ),
inference(superposition,[status(thm)],[c_446,c_64]) ).
tcf(c_1267,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_18))
| ~ theorem(or(iPr_def_12,or(X0,iPr_def_17))) ),
inference(superposition,[status(thm)],[c_447,c_64]) ).
tcf(c_1272,plain,
( theorem(or(p,iPr_def_18))
| ~ theorem(or(iPr_def_12,or(p,iPr_def_17))) ),
inference(instantiation,[status(thm)],[c_1267]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(or(X1,X0)),X1))),
inference(superposition,[status(thm)],[c_104,c_448]) ).
tcf(c_1743,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_17))
| ~ theorem(or(X0,iPr_def_16)) ),
inference(superposition,[status(thm)],[c_315,c_1260]) ).
tcf(c_2255,plain,
! [X0: $i,X1: $i] : theorem(or(or(not(or(X0,X1)),X0),X1)),
inference(superposition,[status(thm)],[c_1427,c_358]) ).
tcf(c_3685,plain,
! [X0: $i] :
( theorem(or(not(or(iPr_def_12,X0)),iPr_def_18))
| ~ theorem(or(not(X0),iPr_def_17)) ),
inference(superposition,[status(thm)],[c_653,c_64]) ).
tcf(c_4108,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X2,X1))
| ~ theorem(or(X2,X0))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_654,c_64]) ).
tcf(c_4110,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_654,c_448]) ).
tcf(c_5183,plain,
! [X0: $i] :
( theorem(iPr_def_18)
| ~ theorem(or(iPr_def_12,X0))
| ~ theorem(or(not(X0),iPr_def_17)) ),
inference(superposition,[status(thm)],[c_3685,c_64]) ).
tcf(c_5187,plain,
! [X0: $i] :
( ~ theorem(or(iPr_def_12,X0))
| ~ theorem(or(not(X0),iPr_def_17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5183,c_151]) ).
tcf(c_7188,plain,
! [X0: $i,X1: $i] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_94,c_4108]) ).
tcf(c_7199,plain,
! [X0: $i] :
( theorem(or(X0,or(q,p)))
| ~ theorem(or(X0,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_346,c_4108]) ).
tcf(c_8835,plain,
! [X0: $i] : theorem(or(or(not(or(X0,iPr_def_16)),X0),iPr_def_17)),
inference(superposition,[status(thm)],[c_2255,c_1743]) ).
tcf(c_12158,plain,
! [X0: $i] : theorem(or(iPr_def_17,or(not(or(X0,iPr_def_16)),X0))),
inference(superposition,[status(thm)],[c_8835,c_358]) ).
tcf(c_15207,plain,
! [X0: $i] : theorem(or(not(or(X0,iPr_def_16)),or(iPr_def_17,X0))),
inference(superposition,[status(thm)],[c_12158,c_448]) ).
tcf(c_38608,plain,
theorem(or(not(or(iPr_def_17,iPr_def_16)),iPr_def_17)),
inference(superposition,[status(thm)],[c_15207,c_7188]) ).
tcf(c_46794,plain,
( theorem(or(q,iPr_def_11))
| ~ theorem(or(iPr_def_10,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_7199,c_1244]) ).
tcf(c_46810,plain,
theorem(or(q,iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_46794,c_316]) ).
tcf(c_46915,plain,
theorem(or(iPr_def_11,q)),
inference(superposition,[status(thm)],[c_46810,c_358]) ).
tcf(c_58322,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2)
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_4110,c_64]) ).
tcf(c_58961,plain,
! [X0: $i,X1: $i] :
( ~ theorem(X0)
| ~ theorem(or(not(X1),iPr_def_17))
| ~ theorem(or(iPr_def_12,or(not(X0),X1))) ),
inference(superposition,[status(thm)],[c_58322,c_5187]) ).
tcf(c_60035,plain,
! [X0: $i,X1: $i] :
( ~ theorem(or(iPr_def_12,X0))
| ~ theorem(or(not(X1),iPr_def_17))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_4110,c_58961]) ).
tcf(c_60260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ theorem(or(not(X2),X1))
| ~ theorem(or(iPr_def_12,or(X0,X2)))
| ~ theorem(or(not(or(X0,X1)),iPr_def_17)) ),
inference(superposition,[status(thm)],[c_654,c_60035]) ).
tcf(c_89557,plain,
! [X0: $i] :
( ~ theorem(or(not(X0),iPr_def_16))
| ~ theorem(or(iPr_def_12,or(iPr_def_17,X0))) ),
inference(superposition,[status(thm)],[c_38608,c_60260]) ).
tcf(c_89733,plain,
( ~ theorem(or(not(p),iPr_def_16))
| ~ theorem(or(iPr_def_12,or(iPr_def_17,p))) ),
inference(instantiation,[status(thm)],[c_89557]) ).
tcf(c_116743,plain,
theorem(or(not(r),iPr_def_16)),
inference(superposition,[status(thm)],[c_148,c_99]) ).
tcf(c_116750,plain,
theorem(or(not(iPr_def_13),or(q,p))),
inference(superposition,[status(thm)],[c_145,c_104]) ).
tcf(c_116752,plain,
theorem(or(not(iPr_def_11),or(p,iPr_def_10))),
inference(superposition,[status(thm)],[c_143,c_104]) ).
tcf(c_116757,plain,
theorem(or(not(or(r,p)),iPr_def_16)),
inference(superposition,[status(thm)],[c_148,c_104]) ).
tcf(c_116763,plain,
theorem(or(iPr_def_12,or(p,iPr_def_10))),
inference(light_normalisation,[status(thm)],[c_116752,c_144]) ).
tcf(c_116767,plain,
! [X0: $i] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_94,c_64]) ).
tcf(c_116768,plain,
! [X0: $i,X1: $i] :
( theorem(or(X1,X0))
| ~ theorem(X0) ),
inference(superposition,[status(thm)],[c_99,c_64]) ).
tcf(c_116769,plain,
! [X0: $i,X1: $i] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_104,c_64]) ).
tcf(c_116831,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_10,or(X0,p))),or(X0,iPr_def_11))),
inference(superposition,[status(thm)],[c_143,c_109]) ).
tcf(c_116833,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_15,or(X0,iPr_def_16))),or(X0,iPr_def_17))),
inference(superposition,[status(thm)],[c_149,c_109]) ).
tcf(c_116834,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_12,or(X0,iPr_def_17))),or(X0,iPr_def_18))),
inference(superposition,[status(thm)],[c_150,c_109]) ).
tcf(c_116835,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_109,c_64]) ).
tcf(c_116963,plain,
! [X0: $i,X1: $i] : theorem(or(not(or(iPr_def_10,X0)),or(not(or(X1,q)),or(X1,X0)))),
inference(superposition,[status(thm)],[c_142,c_114]) ).
tcf(c_116964,plain,
! [X0: $i,X1: $i] : theorem(or(not(or(iPr_def_12,X0)),or(not(or(X1,iPr_def_11)),or(X1,X0)))),
inference(superposition,[status(thm)],[c_144,c_114]) ).
tcf(c_116968,plain,
! [X0: $i] : theorem(or(not(or(not(p),X0)),or(not(iPr_def_11),or(iPr_def_10,X0)))),
inference(superposition,[status(thm)],[c_143,c_114]) ).
tcf(c_116969,plain,
! [X0: $i] : theorem(or(not(or(not(r),X0)),or(not(iPr_def_14),or(iPr_def_13,X0)))),
inference(superposition,[status(thm)],[c_146,c_114]) ).
tcf(c_116978,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_114,c_64]) ).
tcf(c_116980,plain,
! [X0: $i] : theorem(or(not(or(not(r),X0)),or(iPr_def_15,or(iPr_def_13,X0)))),
inference(light_normalisation,[status(thm)],[c_116969,c_147]) ).
tcf(c_116981,plain,
! [X0: $i] : theorem(or(not(or(not(p),X0)),or(iPr_def_12,or(iPr_def_10,X0)))),
inference(light_normalisation,[status(thm)],[c_116968,c_144]) ).
tcf(c_117386,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_11))
| ~ theorem(or(iPr_def_10,or(X0,p))) ),
inference(superposition,[status(thm)],[c_116831,c_64]) ).
tcf(c_117432,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_17))
| ~ theorem(or(iPr_def_15,or(X0,iPr_def_16))) ),
inference(superposition,[status(thm)],[c_116833,c_64]) ).
tcf(c_117469,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_18))
| ~ theorem(or(iPr_def_12,or(X0,iPr_def_17))) ),
inference(superposition,[status(thm)],[c_116834,c_64]) ).
tcf(c_117512,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))),
inference(superposition,[status(thm)],[c_94,c_116835]) ).
tcf(c_117513,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(X1),X1))),
inference(superposition,[status(thm)],[c_99,c_116835]) ).
tcf(c_117514,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(or(X1,X0)),X1))),
inference(superposition,[status(thm)],[c_104,c_116835]) ).
tcf(c_117846,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_11))
| ~ theorem(or(X0,p)) ),
inference(superposition,[status(thm)],[c_116768,c_117386]) ).
tcf(c_117869,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_17))
| ~ theorem(or(X0,iPr_def_16)) ),
inference(superposition,[status(thm)],[c_116768,c_117432]) ).
tcf(c_117887,plain,
! [X0: $i] : theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_117513,c_116767]) ).
tcf(c_117902,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(or(X0,X1)),X1))),
inference(superposition,[status(thm)],[c_117887,c_116835]) ).
tcf(c_117940,plain,
! [X0: $i,X1: $i] :
( theorem(or(not(or(X1,q)),or(X1,X0)))
| ~ theorem(or(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_116963,c_64]) ).
tcf(c_117985,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_18))
| ~ theorem(or(X0,iPr_def_17)) ),
inference(superposition,[status(thm)],[c_116768,c_117469]) ).
tcf(c_118090,plain,
! [X0: $i,X1: $i] :
( theorem(or(not(or(X1,iPr_def_11)),or(X1,X0)))
| ~ theorem(or(iPr_def_12,X0)) ),
inference(superposition,[status(thm)],[c_116964,c_64]) ).
tcf(c_118120,plain,
! [X0: $i] :
( theorem(or(iPr_def_15,or(iPr_def_13,X0)))
| ~ theorem(or(not(r),X0)) ),
inference(superposition,[status(thm)],[c_116980,c_64]) ).
tcf(c_118128,plain,
! [X0: $i] :
( theorem(or(iPr_def_12,or(iPr_def_10,X0)))
| ~ theorem(or(not(p),X0)) ),
inference(superposition,[status(thm)],[c_116981,c_64]) ).
tcf(c_118233,plain,
! [X0: $i,X1: $i] : theorem(or(or(not(or(X0,X1)),X0),X1)),
inference(superposition,[status(thm)],[c_117514,c_116769]) ).
tcf(c_118949,plain,
( theorem(or(iPr_def_13,iPr_def_17))
| ~ theorem(or(not(r),iPr_def_16)) ),
inference(superposition,[status(thm)],[c_118120,c_117432]) ).
tcf(c_118950,plain,
theorem(or(iPr_def_13,iPr_def_17)),
inference(forward_subsumption_resolution,[status(thm)],[c_118949,c_116743]) ).
tcf(c_118958,plain,
theorem(or(iPr_def_17,iPr_def_13)),
inference(superposition,[status(thm)],[c_118950,c_116769]) ).
tcf(c_119041,plain,
( theorem(or(iPr_def_10,iPr_def_18))
| ~ theorem(or(not(p),iPr_def_17)) ),
inference(superposition,[status(thm)],[c_118128,c_117469]) ).
tcf(c_119260,plain,
! [X0: $i,X1: $i] : theorem(or(or(not(or(X0,X1)),X1),X0)),
inference(superposition,[status(thm)],[c_117902,c_116769]) ).
tcf(c_119807,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X2,X1))
| ~ theorem(or(X2,X0))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_116978,c_64]) ).
tcf(c_120047,plain,
! [X0: $i] : theorem(or(or(not(or(X0,p)),X0),iPr_def_11)),
inference(superposition,[status(thm)],[c_118233,c_117846]) ).
tcf(c_120372,plain,
! [X0: $i] : theorem(or(or(not(or(iPr_def_17,X0)),X0),iPr_def_18)),
inference(superposition,[status(thm)],[c_119260,c_117985]) ).
tcf(c_120630,plain,
! [X0: $i] : theorem(or(iPr_def_11,or(not(or(X0,p)),X0))),
inference(superposition,[status(thm)],[c_120047,c_116769]) ).
tcf(c_121211,plain,
! [X0: $i,X1: $i] :
( theorem(or(X0,X1))
| ~ theorem(or(iPr_def_10,X1))
| ~ theorem(or(X0,q)) ),
inference(superposition,[status(thm)],[c_117940,c_64]) ).
tcf(c_121529,plain,
! [X0: $i,X1: $i] :
( theorem(or(X0,X1))
| ~ theorem(or(iPr_def_12,X1))
| ~ theorem(or(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_118090,c_64]) ).
tcf(c_121970,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X0,or(X2,X1)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_104,c_119807]) ).
tcf(c_121979,plain,
! [X0: $i] :
( theorem(or(X0,or(q,p)))
| ~ theorem(or(X0,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_116750,c_119807]) ).
tcf(c_121984,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_16))
| ~ theorem(or(X0,or(r,p))) ),
inference(superposition,[status(thm)],[c_116757,c_119807]) ).
tcf(c_123775,plain,
theorem(or(p,or(not(or(iPr_def_13,iPr_def_13)),q))),
inference(superposition,[status(thm)],[c_145,c_117512]) ).
tcf(c_123846,plain,
theorem(or(or(not(or(iPr_def_13,iPr_def_13)),q),p)),
inference(superposition,[status(thm)],[c_123775,c_116769]) ).
tcf(c_124250,plain,
! [X0: $i] : theorem(or(iPr_def_18,or(not(or(iPr_def_17,X0)),X0))),
inference(superposition,[status(thm)],[c_120372,c_116769]) ).
tcf(c_125455,plain,
! [X0: $i] : theorem(or(not(or(X0,p)),or(iPr_def_11,X0))),
inference(superposition,[status(thm)],[c_120630,c_116835]) ).
tcf(c_127640,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_17,X0)),or(iPr_def_18,X0))),
inference(superposition,[status(thm)],[c_124250,c_116835]) ).
tcf(c_127764,plain,
! [X0: $i] :
( theorem(or(iPr_def_11,X0))
| ~ theorem(or(X0,p)) ),
inference(superposition,[status(thm)],[c_125455,c_64]) ).
tcf(c_128199,plain,
theorem(or(iPr_def_11,or(not(or(iPr_def_13,iPr_def_13)),q))),
inference(superposition,[status(thm)],[c_123846,c_127764]) ).
tcf(c_130386,plain,
! [X0: $i] :
( theorem(or(iPr_def_18,X0))
| ~ theorem(or(iPr_def_17,X0)) ),
inference(superposition,[status(thm)],[c_127640,c_64]) ).
tcf(c_131307,plain,
theorem(or(not(or(iPr_def_13,iPr_def_13)),or(iPr_def_11,q))),
inference(superposition,[status(thm)],[c_128199,c_116835]) ).
tcf(c_132065,plain,
( theorem(or(iPr_def_11,q))
| ~ theorem(or(iPr_def_13,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_131307,c_64]) ).
tcf(c_132177,plain,
theorem(or(iPr_def_11,q)),
inference(global_subsumption_just,[status(thm)],[c_132065,c_46915]) ).
tcf(c_132181,plain,
! [X0: $i] :
( theorem(or(iPr_def_11,X0))
| ~ theorem(or(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_132177,c_121211]) ).
tcf(c_197455,plain,
( theorem(or(iPr_def_18,or(q,p)))
| ~ theorem(or(iPr_def_17,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_121979,c_130386]) ).
tcf(c_197470,plain,
theorem(or(iPr_def_18,or(q,p))),
inference(forward_subsumption_resolution,[status(thm)],[c_197455,c_118958]) ).
tcf(c_197533,plain,
theorem(or(q,or(iPr_def_18,p))),
inference(superposition,[status(thm)],[c_197470,c_116835]) ).
tcf(c_200093,plain,
theorem(or(not(p),iPr_def_16)),
inference(superposition,[status(thm)],[c_99,c_121984]) ).
tcf(c_200293,plain,
theorem(or(not(p),iPr_def_17)),
inference(superposition,[status(thm)],[c_200093,c_117869]) ).
tcf(c_200304,plain,
theorem(or(iPr_def_10,iPr_def_18)),
inference(backward_subsumption_resolution,[status(thm)],[c_119041,c_200293]) ).
tcf(c_200372,plain,
theorem(or(iPr_def_11,iPr_def_18)),
inference(superposition,[status(thm)],[c_200304,c_132181]) ).
tcf(c_200379,plain,
theorem(or(iPr_def_18,iPr_def_11)),
inference(superposition,[status(thm)],[c_200372,c_116769]) ).
tcf(c_200387,plain,
! [X0: $i] :
( theorem(or(iPr_def_18,X0))
| ~ theorem(or(iPr_def_12,X0)) ),
inference(superposition,[status(thm)],[c_200379,c_121529]) ).
tcf(c_201075,plain,
theorem(or(iPr_def_18,or(p,iPr_def_10))),
inference(superposition,[status(thm)],[c_116763,c_200387]) ).
tcf(c_201819,plain,
theorem(or(p,or(iPr_def_18,iPr_def_10))),
inference(superposition,[status(thm)],[c_201075,c_116835]) ).
tcf(c_226428,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_114,c_64]) ).
tcf(c_226843,plain,
! [X0: $i] : theorem(or(not(or(X0,iPr_def_18)),or(iPr_def_12,or(X0,iPr_def_17)))),
inference(superposition,[status(thm)],[c_150,c_109]) ).
tcf(c_227089,plain,
! [X0: $i] :
( theorem(or(iPr_def_12,or(X0,iPr_def_17)))
| ~ theorem(or(X0,iPr_def_18)) ),
inference(superposition,[status(thm)],[c_226843,c_64]) ).
tcf(c_229631,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X2,X1))
| ~ theorem(or(X2,X0))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_226428,c_64]) ).
tcf(c_229652,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X0,or(X2,X1)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_104,c_229631]) ).
tcf(c_251520,plain,
! [X0: $i] :
( theorem(or(iPr_def_12,or(iPr_def_17,X0)))
| ~ theorem(or(X0,iPr_def_18)) ),
inference(superposition,[status(thm)],[c_227089,c_229652]) ).
tcf(c_251889,plain,
( theorem(or(iPr_def_12,or(iPr_def_17,p)))
| ~ theorem(or(p,iPr_def_18)) ),
inference(instantiation,[status(thm)],[c_251520]) ).
tcf(c_261758,plain,
theorem(or(q,or(p,iPr_def_18))),
inference(superposition,[status(thm)],[c_197533,c_121970]) ).
tcf(c_261886,plain,
theorem(or(p,or(iPr_def_10,iPr_def_18))),
inference(superposition,[status(thm)],[c_201819,c_121970]) ).
tcf(c_282527,plain,
theorem(or(or(p,iPr_def_18),q)),
inference(superposition,[status(thm)],[c_261758,c_116769]) ).
tcf(c_292278,plain,
theorem(or(iPr_def_10,or(p,iPr_def_18))),
inference(superposition,[status(thm)],[c_261886,c_116835]) ).
tcf(c_308014,plain,
! [X0: $i] : theorem(or(not(or(X0,iPr_def_18)),or(iPr_def_12,or(X0,iPr_def_17)))),
inference(superposition,[status(thm)],[c_150,c_109]) ).
tcf(c_308034,plain,
! [X0: $i,X1: $i] : theorem(or(not(or(iPr_def_10,X0)),or(not(or(X1,q)),or(X1,X0)))),
inference(superposition,[status(thm)],[c_142,c_114]) ).
tcf(c_308049,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_114,c_64]) ).
tcf(c_308491,plain,
! [X0: $i,X1: $i] :
( theorem(or(not(or(X1,q)),or(X1,X0)))
| ~ theorem(or(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_308034,c_64]) ).
tcf(c_308779,plain,
! [X0: $i,X1: $i,X2: $i] :
( theorem(or(X2,X1))
| ~ theorem(or(X2,X0))
| ~ theorem(or(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_308049,c_64]) ).
tcf(c_309732,plain,
! [X0: $i,X1: $i] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_94,c_308779]) ).
tcf(c_309760,plain,
! [X0: $i,X1: $i] :
( theorem(or(X0,or(iPr_def_12,or(X1,iPr_def_17))))
| ~ theorem(or(X0,or(X1,iPr_def_18))) ),
inference(superposition,[status(thm)],[c_308014,c_308779]) ).
tcf(c_315550,plain,
! [X0: $i] :
( theorem(or(not(or(X0,q)),X0))
| ~ theorem(or(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_308491,c_309732]) ).
tcf(c_327447,plain,
! [X0: $i,X1: $i] :
( theorem(or(iPr_def_12,or(X1,iPr_def_17)))
| ~ theorem(X0)
| ~ theorem(or(not(X0),or(X1,iPr_def_18))) ),
inference(superposition,[status(thm)],[c_309760,c_64]) ).
tcf(c_456885,plain,
! [X0: $i] :
( theorem(or(iPr_def_12,or(X0,iPr_def_17)))
| ~ theorem(or(iPr_def_10,or(X0,iPr_def_18)))
| ~ theorem(or(or(X0,iPr_def_18),q)) ),
inference(superposition,[status(thm)],[c_315550,c_327447]) ).
tcf(c_457226,plain,
( theorem(or(iPr_def_12,or(p,iPr_def_17)))
| ~ theorem(or(iPr_def_10,or(p,iPr_def_18)))
| ~ theorem(or(or(p,iPr_def_18),q)) ),
inference(instantiation,[status(thm)],[c_456885]) ).
tcf(c_457227,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_457226,c_292278,c_282527,c_251889,c_200093,c_89733,c_1272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL222-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.41 % Computer : n002.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Wed Sep 23 22:29:33 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.49
% 0.16/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.49
% 0.16/0.49 % Detected problem language: tptp
% 0.23/0.51 % Proving...
% 178.22/36.72 % SZS status Started for theBenchmark.p
% 178.22/36.72 % SZS status Unsatisfiable for theBenchmark.p
% 178.22/36.72
% 178.22/36.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 178.22/36.72
% 178.22/36.72 % ------ iProver source info
% 178.22/36.72
% 178.22/36.72 % git: date: 2026-07-19 20:42:38 +0200
% 178.22/36.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 178.22/36.72 % git: non_committed_changes: false
% 178.22/36.72
% 178.22/36.72 % ------ Parsing...% successful
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 178.22/36.72
% 178.22/36.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 178.22/36.72
% 178.22/36.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 178.22/36.72
% 178.22/36.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 178.22/36.72 % ------ Proving...
% 178.22/36.72 % ------ Problem Properties
% 178.22/36.72
% 178.22/36.72 %
% 178.22/36.72 % clauses 16
% 178.22/36.72 % conjectures 1
% 178.22/36.72 % EPR 1
% 178.22/36.72 % Horn 16
% 178.22/36.72 % unary 15
% 178.22/36.72 % binary 0
% 178.22/36.72 % lits 18
% 178.22/36.72 % lits eq 9
% 178.22/36.72 % fd_pure 0
% 178.22/36.72 % fd_pseudo 0
% 178.22/36.72 % fd_cond 0
% 178.22/36.72 % fd_pseudo_cond 0
% 178.22/36.72 % AC symbols 0
% 178.22/36.72
% 178.22/36.72 % ------ Schedule dynamic 5 is on
% 178.22/36.72
% 178.22/36.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 % ------
% 178.22/36.72 % Current options:
% 178.22/36.72 % ------
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 %
% 178.22/36.72
% 178.22/36.72 % ------ Proving...
% 178.22/36.72 % Proof_search_loop: time out after: 5709 full_loop iterations
% 178.22/36.72
% 178.22/36.72 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 % ------
% 178.22/36.72 % Current options:
% 178.22/36.72 % ------
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 %
% 178.22/36.72
% 178.22/36.72 % ------ Proving...
% 178.22/36.72 % Proof_search_loop: time out after: 9020 full_loop iterations
% 178.22/36.72
% 178.22/36.72 % ------ Option_1: Negative Selections Time Limit: 35.
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 % ------
% 178.22/36.72 % Current options:
% 178.22/36.72 % ------
% 178.22/36.72
% 178.22/36.72
% 178.22/36.72 %
% 178.22/36.72
% 178.22/36.72 % ------ Proving...
% 178.22/36.72 %
% 178.22/36.72
% 178.22/36.72 % SZS status Unsatisfiable for theBenchmark.p
% 178.22/36.72
% 178.22/36.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 178.22/36.73
% 178.22/36.73
%------------------------------------------------------------------------------