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iProver---3.9.4.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : LCL330-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n008.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 02:06:21 PM UTC 2026

% Result   : Unsatisfiable 15.97s 3.28s
% Output   : CNFRefutation 15.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  111 (  73 unt;  13 def)
%            Number of atoms       :  303 (  17 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  105 (  58   ~;  47   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;  14 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  112 (   0 sgn 112   !;   0   ?;  77   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : axiom(implies(or(X0,X0),X0)),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).

fof(f2,axiom,
    ! [X0,X1] : axiom(implies(X0,or(X1,X0))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).

fof(f3,axiom,
    ! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).

fof(f6,axiom,
    ! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',implies_definition) ).

fof(f7,axiom,
    ! [X0] :
      ( ~ axiom(X0)
      | theorem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ~ theorem(X1)
      | ~ theorem(implies(X1,X0))
      | theorem(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_2) ).

fof(f9,axiom,
    ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-1.ax',and_defn) ).

fof(f10,axiom,
    ! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).

fof(f11,negated_conjecture,
    ~ theorem(equivalent(or(p,q),implies(implies(p,q),q))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f12,plain,
    ! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
    inference(definition_unfolding,[],[f10,f9,f6,f6]) ).

fof(f13,plain,
    ! [X0] : axiom(or(not(or(X0,X0)),X0)),
    inference(definition_unfolding,[],[f1,f6]) ).

fof(f14,plain,
    ! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
    inference(definition_unfolding,[],[f2,f6]) ).

fof(f15,plain,
    ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
    inference(definition_unfolding,[],[f3,f6]) ).

fof(f16,plain,
    ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
    inference(definition_unfolding,[],[f4,f6]) ).

fof(f17,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(f18,plain,
    ! [X0,X1] :
      ( ~ theorem(X1)
      | ~ theorem(or(not(X1),X0))
      | theorem(X0) ),
    inference(definition_unfolding,[],[f8,f6]) ).

fof(f19,plain,
    ~ theorem(not(or(not(or(not(or(p,q)),or(not(or(not(p),q)),q))),not(or(not(or(not(or(not(p),q)),q)),or(p,q)))))),
    inference(definition_unfolding,[],[f11,f12,f6,f6]) ).

tcf(c_60,plain,
    ! [X0: $i] : axiom(or(not(or(X0,X0)),X0)),
    inference(cnf_transformation,[],[f13]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i] : axiom(or(not(X0),or(X1,X0))),
    inference(cnf_transformation,[],[f14]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i] : axiom(or(not(or(X0,X1)),or(X1,X0))),
    inference(cnf_transformation,[],[f15]) ).

tcf(c_63,plain,
    ! [X0: $i,X1: $i,X2: $i] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
    inference(cnf_transformation,[],[f16]) ).

tcf(c_64,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,[],[f17]) ).

tcf(c_65,plain,
    ! [X0: $i] :
      ( theorem(X0)
      | ~ axiom(X0) ),
    inference(cnf_transformation,[],[f7]) ).

tcf(c_66,plain,
    ! [X0: $i,X1: $i] :
      ( theorem(X1)
      | ~ theorem(X0)
      | ~ theorem(or(not(X0),X1)) ),
    inference(cnf_transformation,[],[f18]) ).

tcf(c_67,negated_conjecture,
    ~ theorem(not(or(not(or(not(or(p,q)),or(not(or(not(p),q)),q))),not(or(not(or(not(or(not(p),q)),q)),or(p,q)))))),
    inference(cnf_transformation,[],[f19]) ).

tcf(c_96,plain,
    ! [X0: $i] : theorem(or(not(or(X0,X0)),X0)),
    inference(resolution,[status(thm)],[c_65,c_60]) ).

tcf(c_101,plain,
    ! [X0: $i,X1: $i] : theorem(or(not(X0),or(X1,X0))),
    inference(resolution,[status(thm)],[c_65,c_61]) ).

tcf(c_106,plain,
    ! [X0: $i,X1: $i] : theorem(or(not(or(X0,X1)),or(X1,X0))),
    inference(resolution,[status(thm)],[c_65,c_62]) ).

tcf(c_111,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_65,c_63]) ).

tcf(c_116,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_65,c_64]) ).

tcf(c_144,definition,
    iPr_def_10 = or(p,q),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_145,definition,
    iPr_def_11 = not(iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_146,definition,
    iPr_def_12 = not(p),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_147,definition,
    iPr_def_13 = or(iPr_def_12,q),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_148,definition,
    iPr_def_14 = not(iPr_def_13),
    introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).

tcf(c_149,definition,
    iPr_def_15 = or(iPr_def_14,q),
    introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).

tcf(c_150,definition,
    iPr_def_16 = or(iPr_def_11,iPr_def_15),
    introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).

tcf(c_151,definition,
    iPr_def_17 = not(iPr_def_16),
    introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).

tcf(c_152,definition,
    iPr_def_18 = not(iPr_def_15),
    introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).

tcf(c_153,definition,
    iPr_def_19 = or(iPr_def_18,iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).

tcf(c_154,definition,
    iPr_def_20 = not(iPr_def_19),
    introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).

tcf(c_155,definition,
    iPr_def_21 = or(iPr_def_17,iPr_def_20),
    introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).

tcf(c_156,definition,
    iPr_def_22 = not(iPr_def_21),
    introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).

tcf(c_157,negated_conjecture,
    ~ theorem(iPr_def_22),
    inference(demodulation,[status(thm)],[c_67,c_152,c_153,c_154,c_146,c_147,c_148,c_149,c_144,c_145,c_150,c_151,c_155,c_156]) ).

tcf(c_306,plain,
    ! [X0: $i] : theorem(or(iPr_def_12,or(X0,p))),
    inference(superposition,[status(thm)],[c_146,c_101]) ).

tcf(c_308,plain,
    ! [X0: $i] : theorem(or(iPr_def_14,or(X0,iPr_def_13))),
    inference(superposition,[status(thm)],[c_148,c_101]) ).

tcf(c_315,plain,
    theorem(or(not(q),iPr_def_15)),
    inference(superposition,[status(thm)],[c_149,c_101]) ).

tcf(c_334,plain,
    theorem(or(not(iPr_def_21),or(iPr_def_20,iPr_def_17))),
    inference(superposition,[status(thm)],[c_155,c_106]) ).

tcf(c_336,plain,
    theorem(or(not(or(q,iPr_def_12)),iPr_def_13)),
    inference(superposition,[status(thm)],[c_147,c_106]) ).

tcf(c_341,plain,
    theorem(or(iPr_def_22,or(iPr_def_20,iPr_def_17))),
    inference(light_normalisation,[status(thm)],[c_334,c_156]) ).

tcf(c_354,plain,
    ! [X0: $i] :
      ( theorem(X0)
      | ~ theorem(or(X0,X0)) ),
    inference(superposition,[status(thm)],[c_96,c_66]) ).

tcf(c_355,plain,
    ! [X0: $i,X1: $i] :
      ( theorem(or(X1,X0))
      | ~ theorem(X0) ),
    inference(superposition,[status(thm)],[c_101,c_66]) ).

tcf(c_356,plain,
    ! [X0: $i,X1: $i] :
      ( theorem(or(X1,X0))
      | ~ theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_106,c_66]) ).

tcf(c_364,plain,
    ! [X0: $i] :
      ( theorem(X0)
      | ~ theorem(iPr_def_16)
      | ~ theorem(or(iPr_def_17,X0)) ),
    inference(superposition,[status(thm)],[c_151,c_66]) ).

tcf(c_366,plain,
    ! [X0: $i] :
      ( theorem(X0)
      | ~ theorem(iPr_def_19)
      | ~ theorem(or(iPr_def_20,X0)) ),
    inference(superposition,[status(thm)],[c_154,c_66]) ).

tcf(c_456,plain,
    ! [X0: $i] : theorem(or(not(or(X0,iPr_def_13)),or(iPr_def_12,or(X0,q)))),
    inference(superposition,[status(thm)],[c_147,c_111]) ).

tcf(c_458,plain,
    ! [X0: $i] : theorem(or(not(or(X0,iPr_def_16)),or(iPr_def_11,or(X0,iPr_def_15)))),
    inference(superposition,[status(thm)],[c_150,c_111]) ).

tcf(c_464,plain,
    ! [X0: $i] : theorem(or(not(or(iPr_def_11,or(X0,iPr_def_15))),or(X0,iPr_def_16))),
    inference(superposition,[status(thm)],[c_150,c_111]) ).

tcf(c_467,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( theorem(or(X1,or(X0,X2)))
      | ~ theorem(or(X0,or(X1,X2))) ),
    inference(superposition,[status(thm)],[c_111,c_66]) ).

tcf(c_604,plain,
    ! [X0: $i,X1: $i] : theorem(or(not(or(iPr_def_12,X0)),or(not(or(X1,p)),or(X1,X0)))),
    inference(superposition,[status(thm)],[c_146,c_116]) ).

tcf(c_611,plain,
    ! [X0: $i] : theorem(or(not(or(not(q),X0)),or(not(iPr_def_10),or(p,X0)))),
    inference(superposition,[status(thm)],[c_144,c_116]) ).

tcf(c_620,plain,
    ! [X0: $i] : theorem(or(not(or(not(X0),iPr_def_15)),or(not(or(iPr_def_11,X0)),iPr_def_16))),
    inference(superposition,[status(thm)],[c_150,c_116]) ).

tcf(c_621,plain,
    ! [X0: $i] : theorem(or(not(or(not(X0),iPr_def_10)),or(not(or(iPr_def_18,X0)),iPr_def_19))),
    inference(superposition,[status(thm)],[c_153,c_116]) ).

tcf(c_629,plain,
    ! [X0: $i] : theorem(or(not(or(not(q),X0)),or(iPr_def_11,or(p,X0)))),
    inference(light_normalisation,[status(thm)],[c_611,c_145]) ).

tcf(c_1462,plain,
    theorem(or(not(or(iPr_def_14,iPr_def_13)),or(iPr_def_12,iPr_def_15))),
    inference(superposition,[status(thm)],[c_149,c_456]) ).

tcf(c_1606,plain,
    ( theorem(or(iPr_def_12,iPr_def_15))
    | ~ theorem(or(iPr_def_14,iPr_def_13)) ),
    inference(superposition,[status(thm)],[c_1462,c_66]) ).

tcf(c_1772,plain,
    ! [X0: $i] :
      ( theorem(or(iPr_def_11,or(X0,iPr_def_15)))
      | ~ theorem(or(X0,iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_458,c_66]) ).

tcf(c_2103,plain,
    ! [X0: $i] :
      ( theorem(or(X0,iPr_def_16))
      | ~ theorem(or(iPr_def_11,or(X0,iPr_def_15))) ),
    inference(superposition,[status(thm)],[c_464,c_66]) ).

tcf(c_2243,plain,
    ! [X0: $i,X1: $i,X2: $i] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))),
    inference(superposition,[status(thm)],[c_116,c_467]) ).

tcf(c_2244,plain,
    ! [X0: $i] : theorem(or(X0,or(iPr_def_12,p))),
    inference(superposition,[status(thm)],[c_306,c_467]) ).

tcf(c_2246,plain,
    ! [X0: $i] : theorem(or(X0,or(iPr_def_14,iPr_def_13))),
    inference(superposition,[status(thm)],[c_308,c_467]) ).

tcf(c_2251,plain,
    theorem(or(iPr_def_20,or(iPr_def_22,iPr_def_17))),
    inference(superposition,[status(thm)],[c_341,c_467]) ).

tcf(c_2257,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( theorem(or(X0,or(X2,X1)))
      | ~ theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_355,c_467]) ).

tcf(c_2538,plain,
    theorem(or(iPr_def_12,p)),
    inference(superposition,[status(thm)],[c_2244,c_354]) ).

tcf(c_2555,plain,
    theorem(or(p,iPr_def_12)),
    inference(superposition,[status(thm)],[c_2538,c_356]) ).

tcf(c_2588,plain,
    theorem(or(iPr_def_14,iPr_def_13)),
    inference(superposition,[status(thm)],[c_2246,c_354]) ).

tcf(c_2598,plain,
    theorem(or(iPr_def_12,iPr_def_15)),
    inference(backward_subsumption_resolution,[status(thm)],[c_1606,c_2588]) ).

tcf(c_2614,plain,
    ! [X0: $i,X1: $i] :
      ( theorem(or(not(or(X1,p)),or(X1,X0)))
      | ~ theorem(or(iPr_def_12,X0)) ),
    inference(superposition,[status(thm)],[c_604,c_66]) ).

tcf(c_2859,plain,
    ( theorem(or(iPr_def_22,iPr_def_17))
    | ~ theorem(iPr_def_19) ),
    inference(superposition,[status(thm)],[c_2251,c_366]) ).

tcf(c_3302,plain,
    ( theorem(or(iPr_def_17,iPr_def_22))
    | ~ theorem(iPr_def_19) ),
    inference(superposition,[status(thm)],[c_2859,c_356]) ).

tcf(c_3603,plain,
    ( theorem(iPr_def_22)
    | ~ theorem(iPr_def_19)
    | ~ theorem(iPr_def_16) ),
    inference(superposition,[status(thm)],[c_3302,c_364]) ).

tcf(c_3604,plain,
    ( ~ theorem(iPr_def_19)
    | ~ theorem(iPr_def_16) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3603,c_157]) ).

tcf(c_3989,plain,
    ! [X0: $i] :
      ( theorem(or(iPr_def_11,or(p,X0)))
      | ~ theorem(or(not(q),X0)) ),
    inference(superposition,[status(thm)],[c_629,c_66]) ).

tcf(c_4581,plain,
    ! [X0: $i] :
      ( theorem(or(not(or(iPr_def_11,X0)),iPr_def_16))
      | ~ theorem(or(not(X0),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_620,c_66]) ).

tcf(c_4859,plain,
    ! [X0: $i] :
      ( theorem(or(not(or(iPr_def_18,X0)),iPr_def_19))
      | ~ theorem(or(not(X0),iPr_def_10)) ),
    inference(superposition,[status(thm)],[c_621,c_66]) ).

tcf(c_6630,plain,
    ( theorem(or(p,iPr_def_16))
    | ~ theorem(or(not(q),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_3989,c_2103]) ).

tcf(c_6631,plain,
    theorem(or(p,iPr_def_16)),
    inference(forward_subsumption_resolution,[status(thm)],[c_6630,c_315]) ).

tcf(c_6745,plain,
    theorem(or(iPr_def_16,p)),
    inference(superposition,[status(thm)],[c_6631,c_356]) ).

tcf(c_11517,plain,
    ! [X0: $i] :
      ( theorem(iPr_def_16)
      | ~ theorem(or(iPr_def_11,X0))
      | ~ theorem(or(not(X0),iPr_def_15)) ),
    inference(superposition,[status(thm)],[c_4581,c_66]) ).

tcf(c_11598,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( theorem(or(not(or(not(X1),X2)),or(X0,X2)))
      | ~ theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_2243,c_66]) ).

tcf(c_11615,plain,
    ! [X0: $i] :
      ( theorem(iPr_def_19)
      | ~ theorem(or(iPr_def_18,X0))
      | ~ theorem(or(not(X0),iPr_def_10)) ),
    inference(superposition,[status(thm)],[c_4859,c_66]) ).

tcf(c_11912,plain,
    ( theorem(iPr_def_16)
    | ~ theorem(or(iPr_def_11,or(iPr_def_15,iPr_def_15))) ),
    inference(superposition,[status(thm)],[c_96,c_11517]) ).

tcf(c_13259,plain,
    ! [X0: $i,X1: $i] :
      ( theorem(or(X0,X1))
      | ~ theorem(or(iPr_def_12,X1))
      | ~ theorem(or(X0,p)) ),
    inference(superposition,[status(thm)],[c_2614,c_66]) ).

tcf(c_13785,plain,
    ! [X0: $i] :
      ( theorem(or(iPr_def_16,X0))
      | ~ theorem(or(iPr_def_12,X0)) ),
    inference(superposition,[status(thm)],[c_6745,c_13259]) ).

tcf(c_14502,plain,
    ( theorem(iPr_def_16)
    | ~ theorem(or(iPr_def_15,iPr_def_16)) ),
    inference(superposition,[status(thm)],[c_1772,c_11912]) ).

tcf(c_19042,plain,
    ! [X0: $i,X1: $i] :
      ( theorem(or(not(or(iPr_def_14,X1)),or(X0,X1)))
      | ~ theorem(or(X0,iPr_def_13)) ),
    inference(superposition,[status(thm)],[c_148,c_11598]) ).

tcf(c_19047,plain,
    ! [X0: $i] :
      ( theorem(or(not(or(not(X0),q)),iPr_def_10))
      | ~ theorem(or(p,X0)) ),
    inference(superposition,[status(thm)],[c_144,c_11598]) ).

tcf(c_22529,plain,
    ! [X0: $i] :
      ( theorem(or(not(iPr_def_15),or(X0,q)))
      | ~ theorem(or(X0,iPr_def_13)) ),
    inference(superposition,[status(thm)],[c_149,c_19042]) ).

tcf(c_22542,plain,
    ! [X0: $i] :
      ( theorem(or(iPr_def_18,or(X0,q)))
      | ~ theorem(or(X0,iPr_def_13)) ),
    inference(light_normalisation,[status(thm)],[c_22529,c_152]) ).

tcf(c_24508,plain,
    theorem(or(iPr_def_16,iPr_def_15)),
    inference(superposition,[status(thm)],[c_2598,c_13785]) ).

tcf(c_24871,plain,
    theorem(or(iPr_def_15,iPr_def_16)),
    inference(superposition,[status(thm)],[c_24508,c_356]) ).

tcf(c_24878,plain,
    theorem(iPr_def_16),
    inference(backward_subsumption_resolution,[status(thm)],[c_14502,c_24871]) ).

tcf(c_24888,plain,
    ~ theorem(iPr_def_19),
    inference(backward_subsumption_resolution,[status(thm)],[c_3604,c_24878]) ).

tcf(c_24923,plain,
    ! [X0: $i] :
      ( ~ theorem(or(iPr_def_18,X0))
      | ~ theorem(or(not(X0),iPr_def_10)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_11615,c_24888]) ).

tcf(c_25515,plain,
    ! [X0: $i] :
      ( ~ theorem(or(p,X0))
      | ~ theorem(or(iPr_def_18,or(not(X0),q))) ),
    inference(superposition,[status(thm)],[c_19047,c_24923]) ).

tcf(c_26177,plain,
    ! [X0: $i] :
      ( ~ theorem(or(p,X0))
      | ~ theorem(or(not(X0),iPr_def_13)) ),
    inference(superposition,[status(thm)],[c_22542,c_25515]) ).

tcf(c_27715,plain,
    ~ theorem(or(p,or(q,iPr_def_12))),
    inference(superposition,[status(thm)],[c_336,c_26177]) ).

tcf(c_28301,plain,
    ~ theorem(or(p,iPr_def_12)),
    inference(superposition,[status(thm)],[c_2257,c_27715]) ).

tcf(c_28303,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_28301,c_2555]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL330-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37  % Computer : n008.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Wed Sep 23 22:52:39 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41  Running first-order theorem proving
% 0.09/0.41  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42  
% 0.09/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42  
% 0.09/0.42  % Detected problem language: tptp
% 0.09/0.43  % Proving...
% 15.97/3.28  % SZS status Started for theBenchmark.p
% 15.97/3.28  % SZS status Unsatisfiable for theBenchmark.p
% 15.97/3.28  
% 15.97/3.28  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.97/3.28  
% 15.97/3.28  % ------  iProver source info
% 15.97/3.28  
% 15.97/3.28  % git: date: 2026-07-19 20:42:38 +0200
% 15.97/3.28  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.97/3.28  % git: non_committed_changes: false
% 15.97/3.28  
% 15.97/3.28  % ------ Parsing...% successful
% 15.97/3.28  
% 15.97/3.28  
% 15.97/3.28  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 15.97/3.28  
% 15.97/3.28  % ------ 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 % 
% 15.97/3.28  
% 15.97/3.28  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 15.97/3.28  
% 15.97/3.28  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 15.97/3.28  % ------ Proving...
% 15.97/3.28  % ------ Problem Properties 
% 15.97/3.28  
% 15.97/3.28  % 
% 15.97/3.28  % clauses                               20
% 15.97/3.28  % conjectures                           1
% 15.97/3.28  % EPR                                   1
% 15.97/3.28  % Horn                                  20
% 15.97/3.28  % unary                                 19
% 15.97/3.28  % binary                                0
% 15.97/3.28  % lits                                  22
% 15.97/3.28  % lits eq                               13
% 15.97/3.28  % fd_pure                               0
% 15.97/3.28  % fd_pseudo                             0
% 15.97/3.28  % fd_cond                               0
% 15.97/3.28  % fd_pseudo_cond                        0
% 15.97/3.28  % AC symbols                            0
% 15.97/3.28  
% 15.97/3.28  % ------ Schedule dynamic 5 is on 
% 15.97/3.28  
% 15.97/3.28  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.97/3.28  
% 15.97/3.28  
% 15.97/3.28  % ------ 
% 15.97/3.28  % Current options:
% 15.97/3.28  % ------ 
% 15.97/3.28  
% 15.97/3.28  
% 15.97/3.28  % 
% 15.97/3.28  
% 15.97/3.28  % ------ Proving...
% 15.97/3.28  % 
% 15.97/3.28  
% 15.97/3.28  % SZS status Unsatisfiable for theBenchmark.p
% 15.97/3.28  
% 15.97/3.28  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.97/3.28  
% 15.97/3.28  
%------------------------------------------------------------------------------