%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP167-5 : 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 01:31:38 PM UTC 2026
% Result : Unsatisfiable 11.82s 2.65s
% Output : CNFRefutation 11.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?; 40 :)
% 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(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,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f18,axiom,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
fof(f19,axiom,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
fof(f22,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
fof(f23,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(definition_unfolding,[],[f22,f18,f19]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_75,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_76,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_84,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_85,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(inverse(X0),inverse(X1)) = inverse(least_upper_bound(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_88,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a,
inference(cnf_transformation,[],[f23]) ).
tcf(c_107,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(theory_normalisation,[status(thm)],[c_88,c_75,c_73,c_76,c_74]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_71,c_72]) ).
tcf(c_883,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_270,c_70]) ).
tcf(c_884,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_70,c_883]) ).
tcf(c_885,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_71,c_883]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_883,c_883]) ).
tcf(c_968,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_885,c_887]) ).
tcf(c_982,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_968,c_884]) ).
tcf(c_990,plain,
! [X0: $i] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(superposition,[status(thm)],[c_982,c_85]) ).
tcf(c_1077,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(multiply(X0,X1),identity),
inference(superposition,[status(thm)],[c_71,c_84]) ).
tcf(c_1098,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(identity,multiply(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_1077,c_76,c_74,c_75,c_73]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_887,c_883]) ).
tcf(c_1923,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(identity,X0),multiply(greatest_lower_bound(identity,inverse(X0)),X1)) = X1,
inference(superposition,[status(thm)],[c_990,c_1700]) ).
tcf(c_32372,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),greatest_lower_bound(identity,multiply(identity,X0))) = X0,
inference(superposition,[status(thm)],[c_1098,c_1923]) ).
tcf(c_32436,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),greatest_lower_bound(identity,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_32372,c_70]) ).
tcf(c_32500,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_32436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.75 % Computer : n019.cluster.edu
% 0.10/0.75 % Model : x86_64 x86_64
% 0.10/0.75 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.75 % Memory : 8046.5625MB
% 0.10/0.75 % OS : Linux 6.8.0-71-generic
% 0.10/0.75 % CPULimit : 300
% 0.10/0.75 % WCLimit : 300
% 0.10/0.75 % DateTime : Wed Sep 23 13:56:53 UTC 2026
% 0.10/0.75 % CPUTime :
% 0.10/0.75 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.79 Running UEQ theorem proving
% 0.10/0.79 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
% 0.13/0.80
% 0.13/0.80 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.80
% 0.13/0.80 % Detected problem language: tptp
% 0.13/0.81 % Proving...
% 11.82/2.65 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 11.82/2.65 % SZS status Started for theBenchmark.p
% 11.82/2.65 % SZS status Unsatisfiable for theBenchmark.p
% 11.82/2.65
% 11.82/2.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.82/2.65
% 11.82/2.65 % ------ iProver source info
% 11.82/2.65
% 11.82/2.65 % git: date: 2026-07-19 20:42:38 +0200
% 11.82/2.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.82/2.65 % git: non_committed_changes: false
% 11.82/2.65
% 11.82/2.65 % ------ Parsing...% successful
% 11.82/2.65
% 11.82/2.65
% 11.82/2.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.82/2.65
% 11.82/2.65 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 11.82/2.65
% 11.82/2.65 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.82/2.65
% 11.82/2.65 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 11.82/2.65 % ------ Proving...
% 11.82/2.65 % ------ Problem Properties
% 11.82/2.65
% 11.82/2.65 %
% 11.82/2.65 % clauses 19
% 11.82/2.65 % conjectures 1
% 11.82/2.65 % EPR 0
% 11.82/2.65 % Horn 19
% 11.82/2.65 % unary 19
% 11.82/2.65 % binary 0
% 11.82/2.65 % lits 19
% 11.82/2.65 % lits eq 19
% 11.82/2.65 % fd_pure 0
% 11.82/2.65 % fd_pseudo 0
% 11.82/2.65 % fd_cond 0
% 11.82/2.65 % fd_pseudo_cond 0
% 11.82/2.65 % AC symbols 2
% 11.82/2.65
% 11.82/2.65 % ------ Input Options Time Limit: Unbounded
% 11.82/2.65
% 11.82/2.65
% 11.82/2.65 % ------
% 11.82/2.65 % Current options:
% 11.82/2.65 % ------
% 11.82/2.65
% 11.82/2.65
% 11.82/2.65 %
% 11.82/2.65
% 11.82/2.65 % ------ Proving...
% 11.82/2.65 %
% 11.82/2.65
% 11.82/2.65 % SZS status Unsatisfiable for theBenchmark.p
% 11.82/2.65
% 11.82/2.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.82/2.65
% 11.82/2.65
%------------------------------------------------------------------------------