%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP174-1 : 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 : n019.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 01:31:40 PM UTC 2026
% Result : Unsatisfiable 2.93s 1.38s
% Output : CNFRefutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 62 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?; 61 :)
% 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(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
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/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
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) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p05b_1) ).
fof(f18,plain,
a = greatest_lower_bound(identity,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p05b_2) ).
fof(f20,plain,
inverse(a) = greatest_lower_bound(identity,inverse(a)),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
identity != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p05b) ).
tcf(c_67,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
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_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_80,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_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,
greatest_lower_bound(identity,a) = a,
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
identity != a,
inference(cnf_transformation,[],[f21]) ).
tcf(c_217,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_72,c_70]) ).
tcf(c_237,plain,
least_upper_bound(identity,a) = identity,
inference(superposition,[status(thm)],[c_82,c_76]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_217,c_76]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_71,c_77]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_359,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(X0,inverse(a))) = identity,
inference(superposition,[status(thm)],[c_83,c_242]) ).
tcf(c_380,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(inverse(a),X0)) = identity,
inference(superposition,[status(thm)],[c_70,c_359]) ).
tcf(c_500,plain,
! [X0: $i] : least_upper_bound(identity,least_upper_bound(a,X0)) = least_upper_bound(identity,X0),
inference(superposition,[status(thm)],[c_237,c_73]) ).
tcf(c_862,plain,
! [X0: $i] : greatest_lower_bound(least_upper_bound(a,X0),least_upper_bound(identity,X0)) = least_upper_bound(a,X0),
inference(superposition,[status(thm)],[c_500,c_244]) ).
tcf(c_867,plain,
! [X0: $i] : greatest_lower_bound(least_upper_bound(identity,X0),least_upper_bound(a,X0)) = least_upper_bound(a,X0),
inference(theory_normalisation,[status(thm)],[c_862,c_72,c_70,c_73,c_71]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_257,c_67]) ).
tcf(c_1034,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_67,c_1033]) ).
tcf(c_1035,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_68,c_1033]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_1033,c_1033]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_67,c_81]) ).
tcf(c_1428,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_1035,c_1037]) ).
tcf(c_1444,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_1428,c_1034]) ).
tcf(c_1659,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_1037,c_68]) ).
tcf(c_1661,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_1037,c_1428]) ).
tcf(c_1662,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1661,c_1428]) ).
tcf(c_1756,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(X0,X1),inverse(X1)) = least_upper_bound(multiply(X0,inverse(X1)),identity),
inference(superposition,[status(thm)],[c_1659,c_80]) ).
tcf(c_1762,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(X0,X1),inverse(X1)) = least_upper_bound(identity,multiply(X0,inverse(X1))),
inference(theory_normalisation,[status(thm)],[c_1756,c_72,c_70,c_73,c_71]) ).
tcf(c_4580,plain,
! [X0: $i] : greatest_lower_bound(identity,least_upper_bound(a,greatest_lower_bound(identity,X0))) = least_upper_bound(a,greatest_lower_bound(identity,X0)),
inference(superposition,[status(thm)],[c_76,c_867]) ).
tcf(c_6172,plain,
! [X0: $i] : least_upper_bound(identity,multiply(greatest_lower_bound(identity,X0),inverse(a))) = identity,
inference(superposition,[status(thm)],[c_1194,c_380]) ).
tcf(c_7393,plain,
! [X0: $i] : multiply(least_upper_bound(a,greatest_lower_bound(identity,X0)),inverse(a)) = identity,
inference(demodulation,[status(thm)],[c_6172,c_71,c_1762]) ).
tcf(c_7438,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,least_upper_bound(a,greatest_lower_bound(identity,X0))),inverse(a)) = greatest_lower_bound(inverse(a),identity),
inference(superposition,[status(thm)],[c_7393,c_1194]) ).
tcf(c_7451,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,least_upper_bound(a,greatest_lower_bound(identity,X0))),inverse(a)) = greatest_lower_bound(identity,inverse(a)),
inference(theory_normalisation,[status(thm)],[c_7438,c_72,c_70,c_73,c_71]) ).
tcf(c_7452,plain,
inverse(a) = identity,
inference(light_normalisation,[status(thm)],[c_7451,c_83,c_4580,c_7393]) ).
tcf(c_7527,plain,
inverse(identity) = a,
inference(superposition,[status(thm)],[c_7452,c_1662]) ).
tcf(c_7530,plain,
identity = a,
inference(light_normalisation,[status(thm)],[c_7527,c_1444]) ).
tcf(c_7531,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7530,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP174-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 13:58:36 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.44 Running UEQ theorem proving
% 0.17/0.44 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
% 0.17/0.46
% 0.17/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.46
% 0.17/0.46 % Detected problem language: tptp
% 0.17/0.48 % Proving...
% 2.93/1.38 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.93/1.38 % SZS status Started for theBenchmark.p
% 2.93/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 2.93/1.38
% 2.93/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.93/1.38
% 2.93/1.38 % ------ iProver source info
% 2.93/1.38
% 2.93/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 2.93/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.93/1.38 % git: non_committed_changes: false
% 2.93/1.38
% 2.93/1.38 % ------ Parsing...% successful
% 2.93/1.38
% 2.93/1.38
% 2.93/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.93/1.38
% 2.93/1.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.93/1.38
% 2.93/1.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.93/1.38
% 2.93/1.38 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.93/1.38 % ------ Proving...
% 2.93/1.38 % ------ Problem Properties
% 2.93/1.38
% 2.93/1.38 %
% 2.93/1.38 % clauses 18
% 2.93/1.38 % conjectures 1
% 2.93/1.38 % EPR 1
% 2.93/1.38 % Horn 18
% 2.93/1.38 % unary 18
% 2.93/1.38 % binary 0
% 2.93/1.38 % lits 18
% 2.93/1.38 % lits eq 18
% 2.93/1.38 % fd_pure 0
% 2.93/1.38 % fd_pseudo 0
% 2.93/1.38 % fd_cond 0
% 2.93/1.38 % fd_pseudo_cond 0
% 2.93/1.38 % AC symbols 2
% 2.93/1.38
% 2.93/1.38 % ------ Input Options Time Limit: Unbounded
% 2.93/1.38
% 2.93/1.38
% 2.93/1.38 % ------
% 2.93/1.38 % Current options:
% 2.93/1.38 % ------
% 2.93/1.38
% 2.93/1.38
% 2.93/1.38 %
% 2.93/1.38
% 2.93/1.38 % ------ Proving...
% 2.93/1.38 %
% 2.93/1.38
% 2.93/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 2.93/1.38
% 2.93/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.93/1.38
% 2.93/1.38
%------------------------------------------------------------------------------