%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP170-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 01:31:38 PM UTC 2026
% Result : Unsatisfiable 9.21s 12.22s
% Output : CNFRefutation 9.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 72 unt; 5 def)
% Number of atoms : 139 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03a_1) ).
fof(f18,plain,
b = least_upper_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03a_2) ).
fof(f20,plain,
d = least_upper_bound(c,d),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p03a) ).
fof(f22,plain,
multiply(b,d) != least_upper_bound(multiply(a,c),multiply(b,d)),
inference(reorient_equations,[],[f21]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_74,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,plain,
least_upper_bound(a,b) = b,
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,plain,
least_upper_bound(c,d) = d,
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
inference(cnf_transformation,[],[f22]) ).
tcf(c_141,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_142,definition,
iPr_def_11 = multiply(b,d),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_143,definition,
iPr_def_12 = least_upper_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_144,definition,
iPr_def_13 = least_upper_bound(c,d),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_145,definition,
iPr_def_14 = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_146,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_84,c_142,c_141,c_143]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_157,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_162,plain,
iPr_def_13 = d,
inference(demodulation,[status(thm)],[c_83,c_144]) ).
tcf(c_163,plain,
iPr_def_14 = b,
inference(demodulation,[status(thm)],[c_82,c_145]) ).
tcf(c_243,plain,
multiply(iPr_def_14,iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_142,c_162,c_163]) ).
tcf(c_244,plain,
least_upper_bound(c,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_144,c_162]) ).
tcf(c_245,plain,
least_upper_bound(iPr_def_13,c) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_244,c_158,c_160,c_159,c_161]) ).
tcf(c_246,plain,
least_upper_bound(a,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_145,c_163]) ).
tcf(c_247,plain,
least_upper_bound(iPr_def_14,a) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_246,c_158,c_160,c_159,c_161]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
inference(superposition,[status(thm)],[c_158,c_160]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_160,c_154]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_161,c_155]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(superposition,[status(thm)],[c_157,c_158]) ).
tcf(c_298,plain,
! [X0: $i] : multiply(greatest_lower_bound(iPr_def_14,X0),iPr_def_13) = greatest_lower_bound(iPr_def_11,multiply(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_243,c_150]) ).
tcf(c_406,plain,
! [X0: $i] : least_upper_bound(multiply(a,X0),iPr_def_10) = multiply(a,least_upper_bound(X0,c)),
inference(superposition,[status(thm)],[c_141,c_153]) ).
tcf(c_448,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,least_upper_bound(X0,iPr_def_11)) = least_upper_bound(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_143,c_248]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_248,c_154]) ).
tcf(c_529,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,multiply(a,X0)) = multiply(a,least_upper_bound(X0,c)),
inference(theory_normalisation,[status(thm)],[c_406,c_158,c_160,c_159,c_161]) ).
tcf(c_687,plain,
greatest_lower_bound(a,iPr_def_14) = a,
inference(superposition,[status(thm)],[c_247,c_266]) ).
tcf(c_756,plain,
least_upper_bound(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_143,c_276]) ).
tcf(c_838,plain,
least_upper_bound(iPr_def_10,iPr_def_11) = least_upper_bound(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_448,c_276]) ).
tcf(c_918,plain,
greatest_lower_bound(iPr_def_14,a) = a,
inference(theory_normalisation,[status(thm)],[c_687,c_158,c_160,c_159,c_161]) ).
tcf(c_920,plain,
least_upper_bound(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_838,c_756]) ).
tcf(c_4451,plain,
! [X0: $i] : least_upper_bound(iPr_def_11,multiply(greatest_lower_bound(iPr_def_14,X0),iPr_def_13)) = iPr_def_11,
inference(superposition,[status(thm)],[c_298,c_155]) ).
tcf(c_4871,plain,
least_upper_bound(iPr_def_11,multiply(a,iPr_def_13)) = iPr_def_11,
inference(superposition,[status(thm)],[c_918,c_4451]) ).
tcf(c_6139,plain,
least_upper_bound(iPr_def_10,multiply(a,iPr_def_13)) = multiply(a,iPr_def_13),
inference(superposition,[status(thm)],[c_245,c_529]) ).
tcf(c_6407,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,least_upper_bound(X0,multiply(a,iPr_def_13))) = iPr_def_10,
inference(superposition,[status(thm)],[c_6139,c_453]) ).
tcf(c_7936,plain,
greatest_lower_bound(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_4871,c_6407]) ).
tcf(c_8680,plain,
least_upper_bound(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_7936,c_268]) ).
tcf(c_8970,plain,
least_upper_bound(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_8680,c_158,c_160,c_159,c_161]) ).
tcf(c_9160,plain,
iPr_def_11 = iPr_def_12,
inference(superposition,[status(thm)],[c_8970,c_920]) ).
tcf(c_9954,plain,
$false,
inference(superposition,[status(thm)],[c_9160,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/10.39 % Computer : n018.cluster.edu
% 0.08/10.39 % Model : x86_64 x86_64
% 0.08/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.39 % Memory : 8046.5625MB
% 0.08/10.39 % OS : Linux 6.8.0-71-generic
% 0.08/10.39 % CPULimit : 300
% 0.08/10.39 % WCLimit : 300
% 0.08/10.39 % DateTime : Wed Sep 23 13:59:28 UTC 2026
% 0.08/10.39 % CPUTime :
% 0.08/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.42 Running UEQ theorem proving
% 0.14/10.42 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
% 0.14/10.44
% 0.14/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.44
% 0.14/10.44 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 9.21/12.22 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 9.21/12.22 % SZS status Started for theBenchmark.p
% 9.21/12.22 % SZS status Unsatisfiable for theBenchmark.p
% 9.21/12.22
% 9.21/12.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.21/12.22
% 9.21/12.22 % ------ iProver source info
% 9.21/12.22
% 9.21/12.22 % git: date: 2026-07-19 20:42:38 +0200
% 9.21/12.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.21/12.22 % git: non_committed_changes: false
% 9.21/12.22
% 9.21/12.22 % ------ Parsing...% successful
% 9.21/12.22
% 9.21/12.22
% 9.21/12.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.21/12.22
% 9.21/12.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 9.21/12.22
% 9.21/12.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.21/12.22
% 9.21/12.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 9.21/12.22 % ------ Proving...
% 9.21/12.22 % ------ Problem Properties
% 9.21/12.22
% 9.21/12.22 %
% 9.21/12.22 % clauses 23
% 9.21/12.22 % conjectures 1
% 9.21/12.22 % EPR 3
% 9.21/12.22 % Horn 23
% 9.21/12.22 % unary 23
% 9.21/12.22 % binary 0
% 9.21/12.22 % lits 23
% 9.21/12.22 % lits eq 23
% 9.21/12.22 % fd_pure 0
% 9.21/12.22 % fd_pseudo 0
% 9.21/12.22 % fd_cond 0
% 9.21/12.22 % fd_pseudo_cond 0
% 9.21/12.22 % AC symbols 2
% 9.21/12.22
% 9.21/12.22 % ------ Input Options Time Limit: Unbounded
% 9.21/12.22
% 9.21/12.22
% 9.21/12.22 % ------
% 9.21/12.22 % Current options:
% 9.21/12.22 % ------
% 9.21/12.22
% 9.21/12.22
% 9.21/12.22 %
% 9.21/12.22
% 9.21/12.22 % ------ Proving...
% 9.21/12.22 %
% 9.21/12.22
% 9.21/12.22 % SZS status Unsatisfiable for theBenchmark.p
% 9.21/12.22
% 9.21/12.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.21/12.22
% 9.21/12.22
%------------------------------------------------------------------------------