%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP177-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 01:31:41 PM UTC 2026
% Result : Unsatisfiable 34.14s 5.66s
% Output : CNFRefutation 34.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f10,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
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/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,axiom,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_1) ).
fof(f18,plain,
identity = greatest_lower_bound(identity,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_2) ).
fof(f20,plain,
identity = greatest_lower_bound(identity,b),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
greatest_lower_bound(identity,c) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_3) ).
fof(f22,plain,
identity = greatest_lower_bound(identity,c),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p08b) ).
fof(f24,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(reorient_equations,[],[f23]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,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_74,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_76,plain,
! [X0: $i] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,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_83,plain,
greatest_lower_bound(identity,a) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,plain,
greatest_lower_bound(identity,b) = identity,
inference(cnf_transformation,[],[f20]) ).
tcf(c_85,plain,
greatest_lower_bound(identity,c) = identity,
inference(cnf_transformation,[],[f22]) ).
tcf(c_86,negated_conjecture,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != greatest_lower_bound(a,multiply(b,c)),
inference(cnf_transformation,[],[f24]) ).
tcf(c_102,negated_conjecture,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) != greatest_lower_bound(a,multiply(b,c)),
inference(theory_normalisation,[status(thm)],[c_86,c_74,c_72,c_73,c_71]) ).
tcf(c_141,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,a),multiply(b,c)))))) != greatest_lower_bound(a,multiply(b,c)),
inference(demodulation,[status(thm)],[c_102,c_73,c_80,c_82]) ).
tcf(c_142,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),multiply(b,c)))))) != greatest_lower_bound(a,multiply(b,c)),
inference(theory_normalisation,[status(thm)],[c_141,c_73,c_71,c_74,c_72]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_542,c_68]) ).
tcf(c_549,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_69,c_543]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_543,c_543]) ).
tcf(c_623,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_551,c_549]) ).
tcf(c_647,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_623,c_549]) ).
tcf(c_43797,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_43799,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),multiply(b,c))))) != greatest_lower_bound(a,multiply(b,c)),
inference(demodulation,[status(thm)],[c_142,c_76]) ).
tcf(c_43800,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_647,c_69]) ).
tcf(c_43963,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_43800,c_70]) ).
tcf(c_43965,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_43963,c_68]) ).
tcf(c_43969,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_69,c_43965]) ).
tcf(c_45137,plain,
! [X0: $i] : greatest_lower_bound(multiply(X0,identity),multiply(X0,a)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_83,c_80]) ).
tcf(c_45139,plain,
! [X0: $i] : greatest_lower_bound(multiply(X0,identity),multiply(X0,c)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_85,c_80]) ).
tcf(c_45174,plain,
! [X0: $i] : greatest_lower_bound(X0,multiply(X0,c)) = X0,
inference(demodulation,[status(thm)],[c_45139,c_43969]) ).
tcf(c_45176,plain,
! [X0: $i] : greatest_lower_bound(X0,multiply(X0,a)) = X0,
inference(demodulation,[status(thm)],[c_45137,c_43969]) ).
tcf(c_45240,plain,
! [X0: $i] : greatest_lower_bound(multiply(identity,X0),multiply(b,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_84,c_82]) ).
tcf(c_45279,plain,
! [X0: $i] : greatest_lower_bound(X0,multiply(b,X0)) = X0,
inference(demodulation,[status(thm)],[c_45240,c_68]) ).
tcf(c_45306,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,greatest_lower_bound(multiply(X0,c),X1)) = greatest_lower_bound(X0,X1),
inference(superposition,[status(thm)],[c_45174,c_73]) ).
tcf(c_45384,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,greatest_lower_bound(multiply(X0,a),X1)) = greatest_lower_bound(X0,X1),
inference(superposition,[status(thm)],[c_45176,c_73]) ).
tcf(c_45417,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),multiply(b,c)))) != greatest_lower_bound(a,multiply(b,c)),
inference(demodulation,[status(thm)],[c_43799,c_45384]) ).
tcf(c_45460,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,greatest_lower_bound(multiply(b,X0),X1)) = greatest_lower_bound(X0,X1),
inference(superposition,[status(thm)],[c_45279,c_73]) ).
tcf(c_126256,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(multiply(X0,c),X2))) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
inference(superposition,[status(thm)],[c_43797,c_45306]) ).
tcf(c_126574,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,a),multiply(b,c))) != greatest_lower_bound(a,multiply(b,c)),
inference(demodulation,[status(thm)],[c_45417,c_126256]) ).
tcf(c_132917,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_126574,c_45460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP177-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Wed Sep 23 13:59:56 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.31 Running UEQ theorem proving
% 0.02/0.31 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.32
% 0.02/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.32
% 0.02/0.32 % Detected problem language: tptp
% 0.02/0.32 % Proving...
% 34.14/5.66 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 34.14/5.66 % SZS status Started for theBenchmark.p
% 34.14/5.66 % SZS status Unsatisfiable for theBenchmark.p
% 34.14/5.66
% 34.14/5.66 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.14/5.66
% 34.14/5.66 % ------ iProver source info
% 34.14/5.66
% 34.14/5.66 % git: date: 2026-07-19 20:42:38 +0200
% 34.14/5.66 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.14/5.66 % git: non_committed_changes: false
% 34.14/5.66
% 34.14/5.66 % ------ Parsing...% successful
% 34.14/5.66
% 34.14/5.66
% 34.14/5.66 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.14/5.66
% 34.14/5.66 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 34.14/5.66
% 34.14/5.66 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.14/5.66
% 34.14/5.66 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 34.14/5.66 % ------ Proving...
% 34.14/5.66 % ------ Problem Properties
% 34.14/5.66
% 34.14/5.66 %
% 34.14/5.66 % clauses 19
% 34.14/5.66 % conjectures 0
% 34.14/5.66 % EPR 0
% 34.14/5.66 % Horn 19
% 34.14/5.66 % unary 19
% 34.14/5.66 % binary 0
% 34.14/5.66 % lits 19
% 34.14/5.66 % lits eq 19
% 34.14/5.66 % fd_pure 0
% 34.14/5.66 % fd_pseudo 0
% 34.14/5.66 % fd_cond 0
% 34.14/5.66 % fd_pseudo_cond 0
% 34.14/5.66 % AC symbols 2
% 34.14/5.66
% 34.14/5.66 % ------ Input Options Time Limit: Unbounded
% 34.14/5.66
% 34.14/5.66
% 34.14/5.66 % ------
% 34.14/5.66 % Current options:
% 34.14/5.66 % ------
% 34.14/5.66
% 34.14/5.66
% 34.14/5.66 %
% 34.14/5.66
% 34.14/5.66 % ------ Proving...
% 34.14/5.66 %
% 34.14/5.66
% 34.14/5.66 % SZS status Unsatisfiable for theBenchmark.p
% 34.14/5.66
% 34.14/5.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.14/5.66
% 34.14/5.66
%------------------------------------------------------------------------------