%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 01:31:46 PM UTC 2026
% Result : Unsatisfiable 3.05s 6.22s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 55 unt; 4 def)
% Number of atoms : 93 ( 54 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
fof(f17,axiom,
least_upper_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p39a_1) ).
fof(f18,plain,
a = least_upper_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p39a) ).
fof(f20,plain,
inverse(b) != least_upper_bound(inverse(a),inverse(b)),
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_68,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] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
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(a,b) = a,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
inference(cnf_transformation,[],[f20]) ).
tcf(c_138,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_139,definition,
iPr_def_11 = inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_140,definition,
iPr_def_12 = least_upper_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_141,definition,
iPr_def_13 = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_142,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_82,c_139,c_138,c_140]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_144,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_145,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_158,plain,
iPr_def_13 = a,
inference(demodulation,[status(thm)],[c_81,c_141]) ).
tcf(c_246,plain,
inverse(iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_138,c_158]) ).
tcf(c_247,plain,
least_upper_bound(iPr_def_13,b) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_141,c_158]) ).
tcf(c_249,plain,
multiply(iPr_def_11,b) = identity,
inference(superposition,[status(thm)],[c_139,c_144]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_144,c_143]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_251,c_145]) ).
tcf(c_288,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(b,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_249,c_143]) ).
tcf(c_289,plain,
! [X0: $i] : least_upper_bound(multiply(X0,b),identity) = multiply(least_upper_bound(X0,iPr_def_11),b),
inference(superposition,[status(thm)],[c_249,c_147]) ).
tcf(c_291,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(b,X0)) = X0,
inference(demodulation,[status(thm)],[c_288,c_145]) ).
tcf(c_293,plain,
! [X0: $i] : least_upper_bound(identity,multiply(X0,b)) = multiply(least_upper_bound(X0,iPr_def_11),b),
inference(demodulation,[status(thm)],[c_289,c_156]) ).
tcf(c_346,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_144,c_149]) ).
tcf(c_588,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = multiply(b,X0),
inference(superposition,[status(thm)],[c_291,c_252]) ).
tcf(c_1685,plain,
multiply(b,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_588,c_144]) ).
tcf(c_1763,plain,
multiply(iPr_def_11,identity) = iPr_def_11,
inference(superposition,[status(thm)],[c_1685,c_291]) ).
tcf(c_2652,plain,
least_upper_bound(identity,multiply(iPr_def_10,b)) = multiply(iPr_def_12,b),
inference(superposition,[status(thm)],[c_140,c_293]) ).
tcf(c_5166,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_13),b)) = multiply(inverse(iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_247,c_346]) ).
tcf(c_5219,plain,
multiply(iPr_def_12,b) = identity,
inference(demodulation,[status(thm)],[c_5166,c_144,c_246,c_2652]) ).
tcf(c_5464,plain,
multiply(inverse(iPr_def_12),identity) = b,
inference(superposition,[status(thm)],[c_5219,c_252]) ).
tcf(c_5528,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),multiply(identity,X0)) = multiply(b,X0),
inference(superposition,[status(thm)],[c_5464,c_143]) ).
tcf(c_5550,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),X0) = multiply(b,X0),
inference(demodulation,[status(thm)],[c_5528,c_145]) ).
tcf(c_5742,plain,
multiply(b,iPr_def_12) = identity,
inference(superposition,[status(thm)],[c_5550,c_144]) ).
tcf(c_5834,plain,
multiply(iPr_def_11,identity) = iPr_def_12,
inference(superposition,[status(thm)],[c_5742,c_291]) ).
tcf(c_5835,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_5834,c_1763]) ).
tcf(c_5880,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_142,c_5835]) ).
tcf(c_5881,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_5880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n026.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 14:08:34 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.42 Running UEQ theorem proving
% 0.16/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 3.05/6.22 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.05/6.22 % SZS status Started for theBenchmark.p
% 3.05/6.22 % SZS status Unsatisfiable for theBenchmark.p
% 3.05/6.22
% 3.05/6.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.05/6.22
% 3.05/6.22 % ------ iProver source info
% 3.05/6.22
% 3.05/6.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.05/6.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.05/6.22 % git: non_committed_changes: false
% 3.05/6.22
% 3.05/6.22 % ------ Parsing...% successful
% 3.05/6.22
% 3.05/6.22
% 3.05/6.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.05/6.22
% 3.05/6.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.05/6.22
% 3.05/6.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.05/6.22
% 3.05/6.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.05/6.22 % ------ Proving...
% 3.05/6.22 % ------ Problem Properties
% 3.05/6.22
% 3.05/6.22 %
% 3.05/6.22 % clauses 21
% 3.05/6.22 % conjectures 1
% 3.05/6.22 % EPR 2
% 3.05/6.22 % Horn 21
% 3.05/6.22 % unary 21
% 3.05/6.22 % binary 0
% 3.05/6.22 % lits 21
% 3.05/6.22 % lits eq 21
% 3.05/6.22 % fd_pure 0
% 3.05/6.22 % fd_pseudo 0
% 3.05/6.22 % fd_cond 0
% 3.05/6.22 % fd_pseudo_cond 0
% 3.05/6.22 % AC symbols 2
% 3.05/6.22
% 3.05/6.22 % ------ Input Options Time Limit: Unbounded
% 3.05/6.22
% 3.05/6.22
% 3.05/6.22 % ------
% 3.05/6.22 % Current options:
% 3.05/6.22 % ------
% 3.05/6.22
% 3.05/6.22
% 3.05/6.22 %
% 3.05/6.22
% 3.05/6.22 % ------ Proving...
% 3.05/6.22 %
% 3.05/6.22
% 3.05/6.22 % SZS status Unsatisfiable for theBenchmark.p
% 3.05/6.22
% 3.05/6.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.05/6.22
% 3.05/6.22
%------------------------------------------------------------------------------