%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP175-3 : 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 : n005.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 3.68s 1.28s
% Output : CNFRefutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 14 :)
% 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(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(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,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06c_1) ).
fof(f18,plain,
b = least_upper_bound(identity,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06c) ).
fof(f20,plain,
identity != greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),
inference(reorient_equations,[],[f19]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,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_80,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_81,plain,
least_upper_bound(identity,b) = b,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
inference(cnf_transformation,[],[f20]) ).
tcf(c_234,plain,
greatest_lower_bound(identity,b) = identity,
inference(superposition,[status(thm)],[c_81,c_76]) ).
tcf(c_577,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_67,c_78]) ).
tcf(c_594,plain,
multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != identity,
inference(demodulation,[status(thm)],[c_82,c_577]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_66,c_80]) ).
tcf(c_1055,plain,
multiply(inverse(a),multiply(greatest_lower_bound(identity,b),a)) != identity,
inference(demodulation,[status(thm)],[c_594,c_1033]) ).
tcf(c_1056,plain,
$false,
inference(ground_joinability,[status(thm)],[c_1055,c_66,c_67,c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP175-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:58:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.68/1.28 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.68/1.28 % SZS status Started for theBenchmark.p
% 3.68/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.68/1.28
% 3.68/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.68/1.28
% 3.68/1.28 % ------ iProver source info
% 3.68/1.28
% 3.68/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.68/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.68/1.28 % git: non_committed_changes: false
% 3.68/1.28
% 3.68/1.28 % ------ Parsing...% successful
% 3.68/1.28
% 3.68/1.28
% 3.68/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.68/1.28
% 3.68/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.68/1.28
% 3.68/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.68/1.28
% 3.68/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.68/1.28 % ------ Proving...
% 3.68/1.28 % ------ Problem Properties
% 3.68/1.28
% 3.68/1.28 %
% 3.68/1.28 % clauses 17
% 3.68/1.28 % conjectures 1
% 3.68/1.28 % EPR 0
% 3.68/1.28 % Horn 17
% 3.68/1.28 % unary 17
% 3.68/1.28 % binary 0
% 3.68/1.28 % lits 17
% 3.68/1.28 % lits eq 17
% 3.68/1.28 % fd_pure 0
% 3.68/1.28 % fd_pseudo 0
% 3.68/1.28 % fd_cond 0
% 3.68/1.28 % fd_pseudo_cond 0
% 3.68/1.28 % AC symbols 2
% 3.68/1.28
% 3.68/1.28 % ------ Input Options Time Limit: Unbounded
% 3.68/1.28
% 3.68/1.28
% 3.68/1.28 % ------
% 3.68/1.28 % Current options:
% 3.68/1.28 % ------
% 3.68/1.28
% 3.68/1.28
% 3.68/1.28 %
% 3.68/1.28
% 3.68/1.28 % ------ Proving...
% 3.68/1.28 %
% 3.68/1.28
% 3.68/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.68/1.28
% 3.68/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.68/1.28
% 3.68/1.28
%------------------------------------------------------------------------------