%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p 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 : Fri Sep 25 01:52:32 PM UTC 2026
% Result : Unsatisfiable 26.80s 9.98s
% Output : CNFRefutation 26.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 61 unt; 7 def)
% Number of atoms : 101 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq3(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
fof(f4,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f5,axiom,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f7,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f8,axiom,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f9,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f11,axiom,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f23,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f24,axiom,
! [X2,X0,X1] : ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f25,plain,
! [X2,X0,X1] : true = ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true),
inference(reorient_equations,[],[f24]) ).
fof(f28,axiom,
! [X0,X1] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f29,plain,
! [X0,X1] : true = ifeq3(addition(X0,X1),X1,leq(X0,X1),true),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f31,plain,
true != leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)),
inference(reorient_equations,[],[f30]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_80,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_89,plain,
! [X0: $i] : addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f23]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true) = true,
inference(cnf_transformation,[],[f25]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(cnf_transformation,[],[f29]) ).
tcf(c_94,negated_conjecture,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
inference(cnf_transformation,[],[f31]) ).
tcf(c_117,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_89,c_76,c_75]) ).
tcf(c_174,definition,
iPr_def_10 = multiplication(sK1_goals_X1,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_175,definition,
iPr_def_11 = strong_iteration(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_176,definition,
iPr_def_12 = multiplication(sK2_goals_X0,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_177,definition,
iPr_def_13 = multiplication(sK2_goals_X0,sK1_goals_X1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_178,definition,
iPr_def_14 = strong_iteration(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_179,definition,
iPr_def_15 = multiplication(iPr_def_14,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_180,definition,
iPr_def_16 = leq(iPr_def_12,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_181,negated_conjecture,
iPr_def_16 != true,
inference(demodulation,[status(thm)],[c_94,c_177,c_178,c_179,c_174,c_175,c_176,c_180]) ).
tcf(c_182,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true) = true,
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_195,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_197,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_339,plain,
addition(one,multiplication(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_175,c_182]) ).
tcf(c_354,plain,
! [X0: $i] : ifeq3(X0,X0,leq(X0,X0),true) = true,
inference(superposition,[status(thm)],[c_197,c_183]) ).
tcf(c_355,plain,
! [X0: $i] : leq(X0,X0) = true,
inference(demodulation,[status(thm)],[c_354,c_203]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(X0,addition(X1,multiplication(X2,X0))),true,leq(X0,multiplication(strong_iteration(X2),X1)),true) = true,
inference(superposition,[status(thm)],[c_200,c_186]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c_195,c_193]) ).
tcf(c_624,plain,
! [X0: $i] : multiplication(sK1_goals_X1,multiplication(sK2_goals_X0,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_174,c_196]) ).
tcf(c_625,plain,
! [X0: $i] : multiplication(sK2_goals_X0,multiplication(sK1_goals_X1,X0)) = multiplication(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_177,c_196]) ).
tcf(c_846,plain,
multiplication(sK1_goals_X1,iPr_def_12) = multiplication(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_176,c_624]) ).
tcf(c_1004,plain,
multiplication(sK2_goals_X0,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_846,c_625]) ).
tcf(c_44089,plain,
multiplication(sK2_goals_X0,addition(one,multiplication(iPr_def_10,iPr_def_11))) = addition(sK2_goals_X0,multiplication(iPr_def_13,iPr_def_12)),
inference(superposition,[status(thm)],[c_1004,c_557]) ).
tcf(c_44146,plain,
addition(sK2_goals_X0,multiplication(iPr_def_13,iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_44089,c_176,c_339]) ).
tcf(c_45856,plain,
ifeq(leq(iPr_def_12,iPr_def_12),true,leq(iPr_def_12,multiplication(strong_iteration(iPr_def_13),sK2_goals_X0)),true) = true,
inference(superposition,[status(thm)],[c_44146,c_379]) ).
tcf(c_45870,plain,
true = iPr_def_16,
inference(demodulation,[status(thm)],[c_45856,c_201,c_178,c_179,c_180,c_355]) ).
tcf(c_46176,plain,
iPr_def_16 != iPr_def_16,
inference(demodulation,[status(thm)],[c_181,c_45870]) ).
tcf(c_46177,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_46176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 % Computer : n020.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Wed Sep 23 19:07:48 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.46 Running UEQ theorem proving
% 0.11/0.46 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.48
% 0.11/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.48
% 0.11/0.48 % Detected problem language: tptp
% 0.19/0.50 % Proving...
% 26.80/9.98 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 26.80/9.98 % SZS status Started for theBenchmark.p
% 26.80/9.98 % SZS status Unsatisfiable for theBenchmark.p
% 26.80/9.98
% 26.80/9.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.80/9.98
% 26.80/9.98 % ------ iProver source info
% 26.80/9.98
% 26.80/9.98 % git: date: 2026-07-19 20:42:38 +0200
% 26.80/9.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.80/9.98 % git: non_committed_changes: false
% 26.80/9.98
% 26.80/9.98 % ------ Parsing...% successful
% 26.80/9.98
% 26.80/9.98
% 26.80/9.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.80/9.98
% 26.80/9.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 26.80/9.98
% 26.80/9.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.80/9.98
% 26.80/9.98 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 26.80/9.98 % ------ Proving...
% 26.80/9.98 % ------ Problem Properties
% 26.80/9.98
% 26.80/9.98 %
% 26.80/9.98 % clauses 30
% 26.80/9.98 % conjectures 1
% 26.80/9.98 % EPR 1
% 26.80/9.98 % Horn 30
% 26.80/9.98 % unary 30
% 26.80/9.98 % binary 0
% 26.80/9.98 % lits 30
% 26.80/9.98 % lits eq 30
% 26.80/9.98 % fd_pure 0
% 26.80/9.98 % fd_pseudo 0
% 26.80/9.98 % fd_cond 0
% 26.80/9.98 % fd_pseudo_cond 0
% 26.80/9.98 % AC symbols 1
% 26.80/9.98
% 26.80/9.98 % ------ Input Options Time Limit: Unbounded
% 26.80/9.98
% 26.80/9.98
% 26.80/9.98 % ------
% 26.80/9.98 % Current options:
% 26.80/9.98 % ------
% 26.80/9.98
% 26.80/9.98
% 26.80/9.98 %
% 26.80/9.98
% 26.80/9.98 % ------ Proving...
% 26.80/9.98 %
% 26.80/9.98
% 26.80/9.98 % SZS status Unsatisfiable for theBenchmark.p
% 26.80/9.98
% 26.80/9.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.80/9.98
% 26.80/9.98
%------------------------------------------------------------------------------