%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP184-3 : 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 : n003.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 01:31:44 PM UTC 2026
% Result : Unsatisfiable 26.96s 4.52s
% Output : CNFRefutation 26.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 66 :)
% 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(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
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(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,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21x) ).
tcf(c_65,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,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_71,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,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_77,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_78,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_79,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_80,negated_conjecture,
multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(cnf_transformation,[],[f17]) ).
tcf(c_96,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(theory_normalisation,[status(thm)],[c_80,c_70,c_68,c_71,c_69]) ).
tcf(c_62500,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_66,c_67]) ).
tcf(c_62536,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_62500,c_65]) ).
tcf(c_62538,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_66,c_62536]) ).
tcf(c_62543,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_62536,c_62536]) ).
tcf(c_62584,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_62538,c_62543]) ).
tcf(c_62637,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_62543,c_66]) ).
tcf(c_62639,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_62543,c_62584]) ).
tcf(c_62640,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_62639,c_62584]) ).
tcf(c_62651,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
inference(superposition,[status(thm)],[c_62584,c_76]) ).
tcf(c_62678,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
inference(superposition,[status(thm)],[c_62584,c_77]) ).
tcf(c_62702,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_65,c_78]) ).
tcf(c_62734,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_65,c_79]) ).
tcf(c_62781,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_62637,c_67]) ).
tcf(c_63007,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(superposition,[status(thm)],[c_62781,c_62536]) ).
tcf(c_63216,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(demodulation,[status(thm)],[c_63007,c_62584]) ).
tcf(c_63233,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_63216,c_62536]) ).
tcf(c_63635,plain,
! [X0: $i,X1: $i] : least_upper_bound(inverse(X0),inverse(multiply(X1,X0))) = multiply(inverse(X0),least_upper_bound(identity,inverse(X1))),
inference(superposition,[status(thm)],[c_63233,c_62651]) ).
tcf(c_63883,plain,
! [X0: $i] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_66,c_62678]) ).
tcf(c_63910,plain,
! [X0: $i] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_63883,c_71,c_69,c_70,c_68]) ).
tcf(c_64094,plain,
! [X0: $i,X1: $i] : least_upper_bound(inverse(X0),inverse(multiply(X0,X1))) = multiply(least_upper_bound(identity,inverse(X1)),inverse(X0)),
inference(superposition,[status(thm)],[c_63233,c_62702]) ).
tcf(c_64193,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),inverse(X0)) = greatest_lower_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_62637,c_62734]) ).
tcf(c_64219,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),inverse(X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_64193,c_71,c_69,c_70,c_68]) ).
tcf(c_66060,plain,
! [X0: $i] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = multiply(inverse(greatest_lower_bound(identity,X0)),least_upper_bound(identity,inverse(inverse(X0)))),
inference(superposition,[status(thm)],[c_63910,c_63635]) ).
tcf(c_66094,plain,
! [X0: $i] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = multiply(inverse(greatest_lower_bound(identity,X0)),least_upper_bound(identity,X0)),
inference(light_normalisation,[status(thm)],[c_66060,c_62640]) ).
tcf(c_68504,plain,
! [X0: $i] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = multiply(least_upper_bound(identity,inverse(inverse(X0))),inverse(greatest_lower_bound(identity,X0))),
inference(superposition,[status(thm)],[c_64219,c_64094]) ).
tcf(c_68554,plain,
! [X0: $i] : multiply(inverse(greatest_lower_bound(identity,X0)),least_upper_bound(identity,X0)) = multiply(least_upper_bound(identity,X0),inverse(greatest_lower_bound(identity,X0))),
inference(light_normalisation,[status(thm)],[c_68504,c_62640,c_66094]) ).
tcf(c_68557,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_68554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.57 % Computer : n003.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Wed Sep 23 14:04:52 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.61 Running UEQ theorem proving
% 0.09/0.61 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
% 0.09/0.62
% 0.09/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.62
% 0.09/0.62 % Detected problem language: tptp
% 0.13/0.63 % Proving...
% 26.96/4.52 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 26.96/4.52 % SZS status Started for theBenchmark.p
% 26.96/4.52 % SZS status Unsatisfiable for theBenchmark.p
% 26.96/4.52
% 26.96/4.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.96/4.52
% 26.96/4.52 % ------ iProver source info
% 26.96/4.52
% 26.96/4.52 % git: date: 2026-07-19 20:42:38 +0200
% 26.96/4.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.96/4.52 % git: non_committed_changes: false
% 26.96/4.52
% 26.96/4.52 % ------ Parsing...% successful
% 26.96/4.52
% 26.96/4.52
% 26.96/4.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.96/4.52
% 26.96/4.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 26.96/4.52
% 26.96/4.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.96/4.52
% 26.96/4.52 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 26.96/4.52 % ------ Proving...
% 26.96/4.52 % ------ Problem Properties
% 26.96/4.52
% 26.96/4.52 %
% 26.96/4.52 % clauses 16
% 26.96/4.52 % conjectures 1
% 26.96/4.52 % EPR 0
% 26.96/4.52 % Horn 16
% 26.96/4.52 % unary 16
% 26.96/4.52 % binary 0
% 26.96/4.52 % lits 16
% 26.96/4.52 % lits eq 16
% 26.96/4.52 % fd_pure 0
% 26.96/4.52 % fd_pseudo 0
% 26.96/4.52 % fd_cond 0
% 26.96/4.52 % fd_pseudo_cond 0
% 26.96/4.52 % AC symbols 2
% 26.96/4.52
% 26.96/4.52 % ------ Input Options Time Limit: Unbounded
% 26.96/4.52
% 26.96/4.52
% 26.96/4.52 % ------
% 26.96/4.52 % Current options:
% 26.96/4.52 % ------
% 26.96/4.52
% 26.96/4.52
% 26.96/4.52 %
% 26.96/4.52
% 26.96/4.52 % ------ Proving...
% 26.96/4.52 %
% 26.96/4.52
% 26.96/4.52 % SZS status Unsatisfiable for theBenchmark.p
% 26.96/4.52
% 26.96/4.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.96/4.52
% 26.96/4.52
%------------------------------------------------------------------------------