%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP175-1 : 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 : n008.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 1.92s 1.29s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?; 12 :)
% 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(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(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(f17,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06a_1) ).
fof(f18,plain,
b = least_upper_bound(identity,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06a) ).
fof(f20,plain,
multiply(inverse(a),multiply(b,a)) != least_upper_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_77,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_79,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,
least_upper_bound(identity,b) = b,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_67,c_77]) ).
tcf(c_606,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
inference(demodulation,[status(thm)],[c_82,c_589]) ).
tcf(c_706,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_66,c_79]) ).
tcf(c_807,plain,
$false,
inference(ground_joinability,[status(thm)],[c_606,c_81,c_706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP175-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:59:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running UEQ theorem proving
% 0.10/0.40 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...
% 1.92/1.29 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.92/1.29 % SZS status Started for theBenchmark.p
% 1.92/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.92/1.29
% 1.92/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.92/1.29
% 1.92/1.29 % ------ iProver source info
% 1.92/1.29
% 1.92/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.92/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.92/1.29 % git: non_committed_changes: false
% 1.92/1.29
% 1.92/1.29 % ------ Parsing...% successful
% 1.92/1.29
% 1.92/1.29
% 1.92/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.92/1.29
% 1.92/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.92/1.29
% 1.92/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.92/1.29
% 1.92/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.92/1.29 % ------ Proving...
% 1.92/1.29 % ------ Problem Properties
% 1.92/1.29
% 1.92/1.29 %
% 1.92/1.29 % clauses 17
% 1.92/1.29 % conjectures 1
% 1.92/1.29 % EPR 0
% 1.92/1.29 % Horn 17
% 1.92/1.29 % unary 17
% 1.92/1.29 % binary 0
% 1.92/1.29 % lits 17
% 1.92/1.29 % lits eq 17
% 1.92/1.29 % fd_pure 0
% 1.92/1.29 % fd_pseudo 0
% 1.92/1.29 % fd_cond 0
% 1.92/1.29 % fd_pseudo_cond 0
% 1.92/1.29 % AC symbols 2
% 1.92/1.29
% 1.92/1.29 % ------ Input Options Time Limit: Unbounded
% 1.92/1.29
% 1.92/1.29
% 1.92/1.29 % ------
% 1.92/1.29 % Current options:
% 1.92/1.29 % ------
% 1.92/1.29
% 1.92/1.29
% 1.92/1.29 %
% 1.92/1.29
% 1.92/1.29 % ------ Proving...
% 1.92/1.29 %
% 1.92/1.29
% 1.92/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.92/1.29
% 1.92/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.92/1.29
% 1.92/1.29
%------------------------------------------------------------------------------