%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL181-3 : 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 : n003.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 02:05:52 PM UTC 2026
% Result : Unsatisfiable 4.60s 2.11s
% Output : CNFRefutation 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 73 ( 55 unt; 8 def)
% Number of atoms : 165 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 31 ~; 24 |; 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 : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 92 !; 0 ?; 63 :)
% 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,negated_conjecture,
~ theorem(implies(implies(not(p),q),implies(not(q),p))),
file('/export/starexec/sandbox/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(not(p)),q)),or(not(not(q)),p))),
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(not(p)),q)),or(not(not(q)),p))),
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(p),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_143,definition,
iPr_def_11 = not(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_144,definition,
iPr_def_12 = or(iPr_def_11,q),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_145,definition,
iPr_def_13 = not(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_146,definition,
iPr_def_14 = not(q),
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(iPr_def_15,p),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_149,definition,
iPr_def_17 = or(iPr_def_13,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_150,negated_conjecture,
~ theorem(iPr_def_17),
inference(demodulation,[status(thm)],[c_65,c_146,c_147,c_148,c_142,c_143,c_144,c_145,c_149]) ).
tcf(c_282,plain,
! [X0: $i] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_94,c_64]) ).
tcf(c_310,plain,
! [X0: $i] : theorem(or(iPr_def_10,or(X0,p))),
inference(superposition,[status(thm)],[c_142,c_99]) ).
tcf(c_314,plain,
! [X0: $i] : theorem(or(iPr_def_15,or(X0,iPr_def_14))),
inference(superposition,[status(thm)],[c_147,c_99]) ).
tcf(c_357,plain,
theorem(or(not(or(p,iPr_def_15)),iPr_def_16)),
inference(superposition,[status(thm)],[c_148,c_104]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_104,c_64]) ).
tcf(c_481,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_628,plain,
! [X0: $i,X1: $i] : theorem(or(not(or(iPr_def_11,X0)),or(not(or(X1,iPr_def_10)),or(X1,X0)))),
inference(superposition,[status(thm)],[c_143,c_114]) ).
tcf(c_631,plain,
! [X0: $i] : theorem(or(not(or(not(q),X0)),or(not(iPr_def_12),or(iPr_def_11,X0)))),
inference(superposition,[status(thm)],[c_144,c_114]) ).
tcf(c_636,plain,
! [X0: $i] : theorem(or(not(or(not(X0),iPr_def_16)),or(not(or(iPr_def_13,X0)),iPr_def_17))),
inference(superposition,[status(thm)],[c_149,c_114]) ).
tcf(c_637,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_640,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_14,X0)),or(iPr_def_13,or(iPr_def_11,X0)))),
inference(light_normalisation,[status(thm)],[c_631,c_145,c_146]) ).
tcf(c_951,plain,
! [X0: $i] :
( theorem(or(iPr_def_13,or(iPr_def_11,X0)))
| ~ theorem(or(iPr_def_14,X0)) ),
inference(superposition,[status(thm)],[c_640,c_64]) ).
tcf(c_1058,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(X1),X1))),
inference(superposition,[status(thm)],[c_99,c_481]) ).
tcf(c_1062,plain,
! [X0: $i] : theorem(or(X0,or(iPr_def_10,p))),
inference(superposition,[status(thm)],[c_310,c_481]) ).
tcf(c_1066,plain,
! [X0: $i] : theorem(or(X0,or(iPr_def_15,iPr_def_14))),
inference(superposition,[status(thm)],[c_314,c_481]) ).
tcf(c_1261,plain,
theorem(or(iPr_def_10,p)),
inference(superposition,[status(thm)],[c_1062,c_282]) ).
tcf(c_1274,plain,
theorem(or(p,iPr_def_10)),
inference(superposition,[status(thm)],[c_1261,c_359]) ).
tcf(c_1437,plain,
theorem(or(iPr_def_15,iPr_def_14)),
inference(superposition,[status(thm)],[c_1066,c_282]) ).
tcf(c_1446,plain,
theorem(or(iPr_def_14,iPr_def_15)),
inference(superposition,[status(thm)],[c_1437,c_359]) ).
tcf(c_1553,plain,
! [X0: $i] : theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_1058,c_282]) ).
tcf(c_1571,plain,
! [X0: $i,X1: $i] : theorem(or(X0,or(not(or(X0,X1)),X1))),
inference(superposition,[status(thm)],[c_1553,c_481]) ).
tcf(c_1827,plain,
! [X0: $i,X1: $i] :
( theorem(or(not(or(X1,iPr_def_10)),or(X1,X0)))
| ~ theorem(or(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_628,c_64]) ).
tcf(c_3017,plain,
! [X0: $i] :
( theorem(or(not(or(iPr_def_13,X0)),iPr_def_17))
| ~ theorem(or(not(X0),iPr_def_16)) ),
inference(superposition,[status(thm)],[c_636,c_64]) ).
tcf(c_3302,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_637,c_64]) ).
tcf(c_3792,plain,
! [X0: $i] :
( theorem(iPr_def_17)
| ~ theorem(or(iPr_def_13,X0))
| ~ theorem(or(not(X0),iPr_def_16)) ),
inference(superposition,[status(thm)],[c_3017,c_64]) ).
tcf(c_3796,plain,
! [X0: $i] :
( ~ theorem(or(iPr_def_13,X0))
| ~ theorem(or(not(X0),iPr_def_16)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3792,c_150]) ).
tcf(c_4274,plain,
! [X0: $i,X1: $i] :
( theorem(or(X0,X1))
| ~ theorem(or(iPr_def_11,X1))
| ~ theorem(or(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1827,c_64]) ).
tcf(c_4716,plain,
! [X0: $i] :
( theorem(or(p,X0))
| ~ theorem(or(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_1274,c_4274]) ).
tcf(c_5164,plain,
! [X0: $i] :
( theorem(or(X0,iPr_def_16))
| ~ theorem(or(X0,or(p,iPr_def_15))) ),
inference(superposition,[status(thm)],[c_357,c_3302]) ).
tcf(c_7726,plain,
! [X0: $i] : theorem(or(p,or(not(or(iPr_def_11,X0)),X0))),
inference(superposition,[status(thm)],[c_1571,c_4716]) ).
tcf(c_12133,plain,
! [X0: $i] : theorem(or(not(or(iPr_def_11,X0)),or(p,X0))),
inference(superposition,[status(thm)],[c_7726,c_481]) ).
tcf(c_31310,plain,
theorem(or(not(or(iPr_def_11,iPr_def_15)),iPr_def_16)),
inference(superposition,[status(thm)],[c_12133,c_5164]) ).
tcf(c_31492,plain,
~ theorem(or(iPr_def_13,or(iPr_def_11,iPr_def_15))),
inference(superposition,[status(thm)],[c_31310,c_3796]) ).
tcf(c_31689,plain,
~ theorem(or(iPr_def_14,iPr_def_15)),
inference(superposition,[status(thm)],[c_951,c_31492]) ).
tcf(c_31692,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_31689,c_1446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL181-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 22:14:04 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 4.60/2.11 % SZS status Started for theBenchmark.p
% 4.60/2.11 % SZS status Unsatisfiable for theBenchmark.p
% 4.60/2.11
% 4.60/2.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.60/2.11
% 4.60/2.11 % ------ iProver source info
% 4.60/2.11
% 4.60/2.11 % git: date: 2026-07-19 20:42:38 +0200
% 4.60/2.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.60/2.11 % git: non_committed_changes: false
% 4.60/2.11
% 4.60/2.11 % ------ Parsing...% successful
% 4.60/2.11
% 4.60/2.11
% 4.60/2.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.60/2.11
% 4.60/2.11 % ------ 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 %
% 4.60/2.11
% 4.60/2.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.60/2.11
% 4.60/2.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.60/2.11 % ------ Proving...
% 4.60/2.11 % ------ Problem Properties
% 4.60/2.11
% 4.60/2.11 %
% 4.60/2.11 % clauses 15
% 4.60/2.11 % conjectures 1
% 4.60/2.11 % EPR 1
% 4.60/2.11 % Horn 15
% 4.60/2.11 % unary 14
% 4.60/2.11 % binary 0
% 4.60/2.11 % lits 17
% 4.60/2.11 % lits eq 8
% 4.60/2.11 % fd_pure 0
% 4.60/2.11 % fd_pseudo 0
% 4.60/2.11 % fd_cond 0
% 4.60/2.11 % fd_pseudo_cond 0
% 4.60/2.11 % AC symbols 0
% 4.60/2.11
% 4.60/2.11 % ------ Schedule dynamic 5 is on
% 4.60/2.11
% 4.60/2.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.60/2.11
% 4.60/2.11
% 4.60/2.11 % ------
% 4.60/2.11 % Current options:
% 4.60/2.11 % ------
% 4.60/2.11
% 4.60/2.11
% 4.60/2.11 %
% 4.60/2.11
% 4.60/2.11 % ------ Proving...
% 4.60/2.11 %
% 4.60/2.11
% 4.60/2.11 % SZS status Unsatisfiable for theBenchmark.p
% 4.60/2.11
% 4.60/2.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.60/2.11
% 4.60/2.11
%------------------------------------------------------------------------------