%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP181-4 : 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 : n014.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 01:31:42 PM UTC 2026
% Result : Unsatisfiable 35.40s 11.86s
% Output : CNFRefutation 35.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 81 ( 81 unt; 5 def)
% Number of atoms : 121 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
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(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(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
fof(f17,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_1) ).
fof(f18,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_3) ).
fof(f21,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_4) ).
fof(f22,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_5) ).
fof(f23,axiom,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_6) ).
fof(f25,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12x) ).
tcf(c_72,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,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_78,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_83,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_85,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_87,plain,
inverse(identity) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(cnf_transformation,[],[f21]) ).
tcf(c_91,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(cnf_transformation,[],[f22]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] : least_upper_bound(inverse(X0),inverse(X1)) = inverse(greatest_lower_bound(X0,X1)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_94,negated_conjecture,
a != b,
inference(cnf_transformation,[],[f25]) ).
tcf(c_114,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(theory_normalisation,[status(thm)],[c_90,c_78,c_76,c_77,c_75]) ).
tcf(c_115,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(theory_normalisation,[status(thm)],[c_91,c_78,c_76,c_77,c_75]) ).
tcf(c_168,definition,
iPr_def_10 = least_upper_bound(c,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_169,definition,
iPr_def_11 = least_upper_bound(c,b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_170,definition,
iPr_def_12 = greatest_lower_bound(c,a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_171,definition,
iPr_def_13 = greatest_lower_bound(c,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_172,definition,
iPr_def_14 = inverse(identity),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_173,negated_conjecture,
a != b,
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_174,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_115,c_169,c_168]) ).
tcf(c_175,plain,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_114,c_171,c_170]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_177,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_178,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_182,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_83]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] : least_upper_bound(inverse(X0),inverse(X1)) = inverse(greatest_lower_bound(X0,X1)),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_194,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_195,plain,
iPr_def_14 = identity,
inference(demodulation,[status(thm)],[c_87,c_172]) ).
tcf(c_298,plain,
least_upper_bound(c,a) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_168,c_174]) ).
tcf(c_299,plain,
greatest_lower_bound(c,b) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_171,c_175]) ).
tcf(c_300,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_177,c_195]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(iPr_def_14,X1),
inference(superposition,[status(thm)],[c_300,c_176]) ).
tcf(c_304,plain,
! [X0: $i] : multiply(iPr_def_14,X0) = X0,
inference(light_normalisation,[status(thm)],[c_178,c_195]) ).
tcf(c_306,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_14,
inference(superposition,[status(thm)],[c_194,c_300]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(iPr_def_14,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_300,c_180]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),iPr_def_14),
inference(superposition,[status(thm)],[c_300,c_182]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(iPr_def_14,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[c_378,c_189]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_194,c_193]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_194,c_193]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(iPr_def_14,X1),
inference(superposition,[status(thm)],[c_306,c_176]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_636,c_304]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))) = multiply(iPr_def_14,inverse(X1)),
inference(superposition,[status(thm)],[c_193,c_302]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(demodulation,[status(thm)],[c_730,c_193,c_304,c_433]) ).
tcf(c_1175,plain,
! [X0: $i,X1: $i] : multiply(inverse(greatest_lower_bound(X0,X1)),X0) = least_upper_bound(iPr_def_14,multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[c_192,c_340]) ).
tcf(c_2854,plain,
least_upper_bound(iPr_def_14,multiply(inverse(a),c)) = multiply(inverse(a),iPr_def_11),
inference(superposition,[status(thm)],[c_298,c_386]) ).
tcf(c_2855,plain,
least_upper_bound(iPr_def_14,multiply(inverse(b),c)) = multiply(inverse(b),iPr_def_11),
inference(superposition,[status(thm)],[c_169,c_386]) ).
tcf(c_82441,plain,
least_upper_bound(iPr_def_14,multiply(inverse(a),c)) = multiply(inverse(iPr_def_12),c),
inference(superposition,[status(thm)],[c_170,c_1175]) ).
tcf(c_82442,plain,
least_upper_bound(iPr_def_14,multiply(inverse(b),c)) = multiply(inverse(iPr_def_12),c),
inference(superposition,[status(thm)],[c_299,c_1175]) ).
tcf(c_82941,plain,
multiply(inverse(a),iPr_def_11) = multiply(inverse(iPr_def_12),c),
inference(demodulation,[status(thm)],[c_2854,c_82441]) ).
tcf(c_82942,plain,
multiply(inverse(b),iPr_def_11) = multiply(inverse(iPr_def_12),c),
inference(demodulation,[status(thm)],[c_2855,c_82442]) ).
tcf(c_85119,plain,
inverse(multiply(inverse(iPr_def_12),c)) = multiply(inverse(iPr_def_11),a),
inference(superposition,[status(thm)],[c_82941,c_435]) ).
tcf(c_85132,plain,
multiply(inverse(c),iPr_def_12) = multiply(inverse(iPr_def_11),a),
inference(demodulation,[status(thm)],[c_85119,c_435]) ).
tcf(c_85583,plain,
multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_12),c))) = inverse(inverse(b)),
inference(superposition,[status(thm)],[c_82942,c_746]) ).
tcf(c_85663,plain,
a = b,
inference(demodulation,[status(thm)],[c_85583,c_194,c_435,c_644,c_85132]) ).
tcf(c_85664,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_85663,c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 14:01:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running UEQ theorem proving
% 0.10/0.39 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 35.40/11.86 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 35.40/11.86 % SZS status Started for theBenchmark.p
% 35.40/11.86 % SZS status Unsatisfiable for theBenchmark.p
% 35.40/11.86
% 35.40/11.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.40/11.86
% 35.40/11.86 % ------ iProver source info
% 35.40/11.86
% 35.40/11.86 % git: date: 2026-07-19 20:42:38 +0200
% 35.40/11.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.40/11.86 % git: non_committed_changes: false
% 35.40/11.86
% 35.40/11.86 % ------ Parsing...% successful
% 35.40/11.86
% 35.40/11.86
% 35.40/11.86 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.40/11.86
% 35.40/11.86 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 35.40/11.86
% 35.40/11.86 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.40/11.86
% 35.40/11.86 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 35.40/11.86 % ------ Proving...
% 35.40/11.86 % ------ Problem Properties
% 35.40/11.86
% 35.40/11.86 %
% 35.40/11.86 % clauses 28
% 35.40/11.86 % conjectures 1
% 35.40/11.86 % EPR 4
% 35.40/11.86 % Horn 28
% 35.40/11.86 % unary 28
% 35.40/11.86 % binary 0
% 35.40/11.86 % lits 28
% 35.40/11.86 % lits eq 28
% 35.40/11.86 % fd_pure 0
% 35.40/11.86 % fd_pseudo 0
% 35.40/11.86 % fd_cond 0
% 35.40/11.86 % fd_pseudo_cond 0
% 35.40/11.86 % AC symbols 2
% 35.40/11.86
% 35.40/11.86 % ------ Input Options Time Limit: Unbounded
% 35.40/11.86
% 35.40/11.86
% 35.40/11.86 % ------
% 35.40/11.86 % Current options:
% 35.40/11.86 % ------
% 35.40/11.86
% 35.40/11.86
% 35.40/11.86 %
% 35.40/11.86
% 35.40/11.86 % ------ Proving...
% 35.40/11.86 %
% 35.40/11.86
% 35.40/11.86 % SZS status Unsatisfiable for theBenchmark.p
% 35.40/11.86
% 35.40/11.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.40/11.86
% 35.40/11.86
%------------------------------------------------------------------------------