%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL312-3 : 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 : n009.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 02:06:19 PM UTC 2026
% Result : Unsatisfiable 8.39s 1.76s
% Output : CNFRefutation 8.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 54 unt; 10 def)
% Number of atoms : 163 ( 14 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 32 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?; 49 :)
% 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(implies(not(p),p),p)),
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(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p)))))),
inference(definition_unfolding,[],[f11,f12,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(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p)))))),
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 = not(p),
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 = or(iPr_def_11,p),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_147,definition,
iPr_def_13 = not(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_148,definition,
iPr_def_14 = or(iPr_def_13,p),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_149,definition,
iPr_def_15 = not(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_150,definition,
iPr_def_16 = or(iPr_def_10,iPr_def_12),
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 = or(iPr_def_15,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_153,definition,
iPr_def_19 = not(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_154,negated_conjecture,
~ theorem(iPr_def_19),
inference(demodulation,[status(thm)],[c_67,c_150,c_151,c_144,c_145,c_146,c_147,c_148,c_149,c_152,c_153]) ).
tcf(c_298,plain,
! [X0: $i] :
( theorem(X0)
| ~ theorem(iPr_def_14)
| ~ theorem(or(iPr_def_15,X0)) ),
inference(superposition,[status(thm)],[c_149,c_66]) ).
tcf(c_299,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_327,plain,
! [X0: $i] : theorem(or(iPr_def_10,or(X0,p))),
inference(superposition,[status(thm)],[c_144,c_101]) ).
tcf(c_333,plain,
theorem(or(not(p),iPr_def_12)),
inference(superposition,[status(thm)],[c_146,c_101]) ).
tcf(c_340,plain,
theorem(iPr_def_16),
inference(light_normalisation,[status(thm)],[c_333,c_144,c_150]) ).
tcf(c_364,plain,
theorem(or(not(iPr_def_18),or(iPr_def_17,iPr_def_15))),
inference(superposition,[status(thm)],[c_152,c_106]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_106,c_66]) ).
tcf(c_370,plain,
theorem(or(iPr_def_19,or(iPr_def_17,iPr_def_15))),
inference(light_normalisation,[status(thm)],[c_364,c_153]) ).
tcf(c_462,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_648,plain,
! [X0: $i] : theorem(or(not(or(not(X0),p)),or(not(or(iPr_def_13,X0)),iPr_def_14))),
inference(superposition,[status(thm)],[c_148,c_116]) ).
tcf(c_984,plain,
! [X0: $i] :
( theorem(X0)
| ~ theorem(or(iPr_def_17,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_299,c_299,c_340]) ).
tcf(c_1549,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_462]) ).
tcf(c_1550,plain,
! [X0: $i] : theorem(or(X0,or(iPr_def_10,p))),
inference(superposition,[status(thm)],[c_327,c_462]) ).
tcf(c_1558,plain,
theorem(or(iPr_def_17,or(iPr_def_19,iPr_def_15))),
inference(superposition,[status(thm)],[c_370,c_462]) ).
tcf(c_1771,plain,
theorem(or(iPr_def_10,p)),
inference(superposition,[status(thm)],[c_1550,c_984]) ).
tcf(c_1778,plain,
theorem(or(p,iPr_def_10)),
inference(superposition,[status(thm)],[c_1771,c_369]) ).
tcf(c_1958,plain,
theorem(or(iPr_def_19,iPr_def_15)),
inference(superposition,[status(thm)],[c_1558,c_984]) ).
tcf(c_1962,plain,
theorem(or(iPr_def_15,iPr_def_19)),
inference(superposition,[status(thm)],[c_1958,c_369]) ).
tcf(c_1963,plain,
( theorem(iPr_def_19)
| ~ theorem(iPr_def_14) ),
inference(superposition,[status(thm)],[c_1962,c_298]) ).
tcf(c_1965,plain,
~ theorem(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_1963,c_154]) ).
tcf(c_3195,plain,
! [X0: $i] :
( theorem(or(not(or(iPr_def_13,X0)),iPr_def_14))
| ~ theorem(or(not(X0),p)) ),
inference(superposition,[status(thm)],[c_648,c_66]) ).
tcf(c_4338,plain,
! [X0: $i] :
( theorem(iPr_def_14)
| ~ theorem(or(iPr_def_13,X0))
| ~ theorem(or(not(X0),p)) ),
inference(superposition,[status(thm)],[c_3195,c_66]) ).
tcf(c_4343,plain,
! [X0: $i] :
( ~ theorem(or(iPr_def_13,X0))
| ~ theorem(or(not(X0),p)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4338,c_1965]) ).
tcf(c_4381,plain,
~ theorem(or(iPr_def_13,or(p,p))),
inference(superposition,[status(thm)],[c_96,c_4343]) ).
tcf(c_8508,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_1549,c_66]) ).
tcf(c_9236,plain,
! [X0: $i,X1: $i] :
( theorem(or(not(or(iPr_def_11,X1)),or(X0,X1)))
| ~ theorem(or(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_145,c_8508]) ).
tcf(c_10249,plain,
! [X0: $i] :
( theorem(or(not(iPr_def_12),or(X0,p)))
| ~ theorem(or(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_146,c_9236]) ).
tcf(c_10260,plain,
! [X0: $i] :
( theorem(or(iPr_def_13,or(X0,p)))
| ~ theorem(or(X0,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_10249,c_147]) ).
tcf(c_10270,plain,
( theorem(or(iPr_def_13,or(p,p)))
| ~ theorem(or(p,iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_10260]) ).
tcf(c_10271,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10270,c_4381,c_1778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL312-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n009.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 22:48:43 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 8.39/1.76 % SZS status Started for theBenchmark.p
% 8.39/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 8.39/1.76
% 8.39/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.39/1.76
% 8.39/1.76 % ------ iProver source info
% 8.39/1.76
% 8.39/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 8.39/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.39/1.76 % git: non_committed_changes: false
% 8.39/1.76
% 8.39/1.76 % ------ Parsing...% successful
% 8.39/1.76
% 8.39/1.76
% 8.39/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.39/1.76
% 8.39/1.76 % ------ 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 %
% 8.39/1.76
% 8.39/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.39/1.76
% 8.39/1.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.39/1.76 % ------ Proving...
% 8.39/1.76 % ------ Problem Properties
% 8.39/1.76
% 8.39/1.76 %
% 8.39/1.76 % clauses 17
% 8.39/1.76 % conjectures 1
% 8.39/1.76 % EPR 1
% 8.39/1.76 % Horn 17
% 8.39/1.76 % unary 16
% 8.39/1.76 % binary 0
% 8.39/1.76 % lits 19
% 8.39/1.76 % lits eq 10
% 8.39/1.76 % fd_pure 0
% 8.39/1.76 % fd_pseudo 0
% 8.39/1.76 % fd_cond 0
% 8.39/1.76 % fd_pseudo_cond 0
% 8.39/1.76 % AC symbols 0
% 8.39/1.76
% 8.39/1.76 % ------ Schedule dynamic 5 is on
% 8.39/1.76
% 8.39/1.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.39/1.76
% 8.39/1.76
% 8.39/1.76 % ------
% 8.39/1.76 % Current options:
% 8.39/1.76 % ------
% 8.39/1.76
% 8.39/1.76
% 8.39/1.76 %
% 8.39/1.76
% 8.39/1.76 % ------ Proving...
% 8.39/1.76 %
% 8.39/1.76
% 8.39/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 8.39/1.76
% 8.39/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.39/1.77
% 8.39/1.77
%------------------------------------------------------------------------------