%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP191-1 : 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 : n018.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 6.65s 6.75s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 64 ( 64 unt; 4 def)
% Number of atoms : 107 ( 63 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 56 :)
% 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(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,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39b_1) ).
fof(f18,plain,
b = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p39b) ).
fof(f20,plain,
inverse(a) != greatest_lower_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_69,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,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_72,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_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,
greatest_lower_bound(a,b) = b,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
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 = greatest_lower_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_141,definition,
iPr_def_13 = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_142,negated_conjecture,
iPr_def_12 != iPr_def_10,
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_146,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_154,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(demodulation,[status(thm)],[c_72]) ).
tcf(c_155,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(demodulation,[status(thm)],[c_71]) ).
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_157,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_158,plain,
iPr_def_13 = b,
inference(demodulation,[status(thm)],[c_81,c_141]) ).
tcf(c_240,plain,
inverse(iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_139,c_158]) ).
tcf(c_241,plain,
greatest_lower_bound(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_140,c_155,c_157,c_154,c_156]) ).
tcf(c_242,plain,
greatest_lower_bound(a,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_141,c_158]) ).
tcf(c_243,plain,
greatest_lower_bound(iPr_def_13,a) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_242,c_155,c_157,c_154,c_156]) ).
tcf(c_254,plain,
multiply(iPr_def_10,a) = identity,
inference(superposition,[status(thm)],[c_138,c_144]) ).
tcf(c_255,plain,
multiply(iPr_def_11,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_240,c_144]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_144,c_143]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_267,c_145]) ).
tcf(c_498,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(X0,a)) = multiply(greatest_lower_bound(iPr_def_10,X0),a),
inference(superposition,[status(thm)],[c_254,c_146]) ).
tcf(c_608,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,greatest_lower_bound(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_255,c_148]) ).
tcf(c_655,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(a,X0)) = X0,
inference(superposition,[status(thm)],[c_138,c_433]) ).
tcf(c_658,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_144,c_433]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_433,c_433]) ).
tcf(c_1423,plain,
! [X0: $i] : multiply(inverse(iPr_def_10),X0) = multiply(a,X0),
inference(superposition,[status(thm)],[c_655,c_433]) ).
tcf(c_1841,plain,
multiply(a,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_1423,c_144]) ).
tcf(c_2019,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_662,c_658]) ).
tcf(c_4992,plain,
multiply(greatest_lower_bound(iPr_def_10,iPr_def_11),a) = multiply(iPr_def_11,greatest_lower_bound(iPr_def_13,a)),
inference(superposition,[status(thm)],[c_608,c_498]) ).
tcf(c_5333,plain,
multiply(greatest_lower_bound(iPr_def_11,iPr_def_10),a) = multiply(iPr_def_11,greatest_lower_bound(iPr_def_13,a)),
inference(theory_normalisation,[status(thm)],[c_4992,c_155,c_157,c_154,c_156]) ).
tcf(c_5334,plain,
multiply(iPr_def_12,a) = identity,
inference(demodulation,[status(thm)],[c_5333,c_241,c_243,c_255]) ).
tcf(c_5671,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_5334,c_143]) ).
tcf(c_5712,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(a,X0)) = X0,
inference(demodulation,[status(thm)],[c_5671,c_145]) ).
tcf(c_5887,plain,
multiply(iPr_def_12,identity) = iPr_def_10,
inference(superposition,[status(thm)],[c_1841,c_5712]) ).
tcf(c_6076,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_5887,c_2019]) ).
tcf(c_6340,plain,
$false,
inference(superposition,[status(thm)],[c_6076,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP191-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n018.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Wed Sep 23 14:08:08 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running UEQ theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 6.65/6.75 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 6.65/6.75 % SZS status Started for theBenchmark.p
% 6.65/6.75 % SZS status Unsatisfiable for theBenchmark.p
% 6.65/6.75
% 6.65/6.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.65/6.75
% 6.65/6.75 % ------ iProver source info
% 6.65/6.75
% 6.65/6.75 % git: date: 2026-07-19 20:42:38 +0200
% 6.65/6.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.65/6.75 % git: non_committed_changes: false
% 6.65/6.75
% 6.65/6.75 % ------ Parsing...% successful
% 6.65/6.75
% 6.65/6.75
% 6.65/6.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.65/6.75
% 6.65/6.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.65/6.75
% 6.65/6.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.65/6.75
% 6.65/6.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.65/6.75 % ------ Proving...
% 6.65/6.75 % ------ Problem Properties
% 6.65/6.75
% 6.65/6.75 %
% 6.65/6.75 % clauses 21
% 6.65/6.75 % conjectures 1
% 6.65/6.75 % EPR 2
% 6.65/6.75 % Horn 21
% 6.65/6.75 % unary 21
% 6.65/6.75 % binary 0
% 6.65/6.75 % lits 21
% 6.65/6.75 % lits eq 21
% 6.65/6.75 % fd_pure 0
% 6.65/6.75 % fd_pseudo 0
% 6.65/6.75 % fd_cond 0
% 6.65/6.75 % fd_pseudo_cond 0
% 6.65/6.75 % AC symbols 2
% 6.65/6.75
% 6.65/6.75 % ------ Input Options Time Limit: Unbounded
% 6.65/6.75
% 6.65/6.75
% 6.65/6.75 % ------
% 6.65/6.75 % Current options:
% 6.65/6.75 % ------
% 6.65/6.75
% 6.65/6.75
% 6.65/6.75 %
% 6.65/6.75
% 6.65/6.75 % ------ Proving...
% 6.65/6.75 %
% 6.65/6.75
% 6.65/6.75 % SZS status Unsatisfiable for theBenchmark.p
% 6.65/6.75
% 6.65/6.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.65/6.75
% 6.65/6.75
%------------------------------------------------------------------------------