%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP184-4 : 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 : n009.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 01:31:44 PM UTC 2026
% Result : Unsatisfiable 7.43s 2.21s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 113 !; 0 ?; 81 :)
% 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(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
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(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_1) ).
fof(f18,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_3) ).
fof(f21,axiom,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_4) ).
fof(f23,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p21x) ).
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_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_77,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_81,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_83,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_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,
inverse(identity) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_86,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] : least_upper_bound(inverse(X0),inverse(X1)) = inverse(greatest_lower_bound(X0,X1)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_90,negated_conjecture,
multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(cnf_transformation,[],[f23]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(superposition,[status(thm)],[c_75,c_73]) ).
tcf(c_122,plain,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(theory_normalisation,[status(thm)],[c_90,c_75,c_73,c_76,c_74]) ).
tcf(c_124,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_86,c_71]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_73,c_79]) ).
tcf(c_136,plain,
! [X0: $i] : inverse(multiply(identity,X0)) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[c_85,c_87]) ).
tcf(c_142,plain,
! [X0: $i] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
inference(superposition,[status(thm)],[c_85,c_88]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_97,c_79]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_70,c_83]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_70,c_84]) ).
tcf(c_286,plain,
! [X0: $i] : multiply(inverse(X0),identity) = inverse(X0),
inference(demodulation,[status(thm)],[c_136,c_70]) ).
tcf(c_317,plain,
multiply(least_upper_bound(identity,inverse(a)),least_upper_bound(identity,a)) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))),
inference(demodulation,[status(thm)],[c_122,c_142]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2)) = least_upper_bound(X0,X2),
inference(superposition,[status(thm)],[c_125,c_76]) ).
tcf(c_641,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_86,c_286]) ).
tcf(c_693,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),least_upper_bound(identity,inverse(X0))) = identity,
inference(superposition,[status(thm)],[c_142,c_124]) ).
tcf(c_766,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_73,c_190]) ).
tcf(c_1373,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
inference(superposition,[status(thm)],[c_641,c_81]) ).
tcf(c_1421,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(least_upper_bound(X0,X1),greatest_lower_bound(X2,X0)) = least_upper_bound(X0,X1),
inference(superposition,[status(thm)],[c_80,c_766]) ).
tcf(c_1663,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(X2,X0))) = least_upper_bound(X0,X1),
inference(theory_normalisation,[status(thm)],[c_1421,c_75,c_73,c_76,c_74]) ).
tcf(c_4664,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),inverse(X0)) = least_upper_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_124,c_245]) ).
tcf(c_4701,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),inverse(X0)) = greatest_lower_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_124,c_265]) ).
tcf(c_4918,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),inverse(X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_4701,c_75,c_73,c_76,c_74]) ).
tcf(c_4919,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),inverse(X0)) = least_upper_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_4664,c_75,c_73,c_76,c_74]) ).
tcf(c_5232,plain,
! [X0: $i] : multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_71,c_1373]) ).
tcf(c_5394,plain,
! [X0: $i] : multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_5232,c_75,c_73,c_76,c_74]) ).
tcf(c_7681,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),least_upper_bound(identity,inverse(X0))) = least_upper_bound(greatest_lower_bound(identity,X0),greatest_lower_bound(identity,inverse(X0))),
inference(superposition,[status(thm)],[c_4918,c_1373]) ).
tcf(c_7737,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),least_upper_bound(identity,inverse(X0))) = least_upper_bound(least_upper_bound(identity,X0),least_upper_bound(identity,inverse(X0))),
inference(superposition,[status(thm)],[c_4919,c_1373]) ).
tcf(c_7791,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),least_upper_bound(identity,inverse(X0))) = least_upper_bound(identity,least_upper_bound(X0,least_upper_bound(identity,inverse(X0)))),
inference(theory_normalisation,[status(thm)],[c_7737,c_75,c_73,c_76,c_74]) ).
tcf(c_7792,plain,
! [X0: $i] : multiply(least_upper_bound(identity,X0),least_upper_bound(identity,inverse(X0))) = least_upper_bound(identity,least_upper_bound(X0,inverse(X0))),
inference(ac_demodulation,[status(thm)],[c_7791,c_77,c_75,c_73,c_76,c_74]) ).
tcf(c_7799,plain,
! [X0: $i] : least_upper_bound(greatest_lower_bound(identity,X0),greatest_lower_bound(identity,inverse(X0))) = identity,
inference(demodulation,[status(thm)],[c_7681,c_693]) ).
tcf(c_7894,plain,
multiply(least_upper_bound(identity,inverse(a)),least_upper_bound(identity,a)) != least_upper_bound(identity,least_upper_bound(a,inverse(a))),
inference(demodulation,[status(thm)],[c_317,c_7792]) ).
tcf(c_8770,plain,
! [X0: $i] : least_upper_bound(X0,greatest_lower_bound(identity,inverse(X0))) = least_upper_bound(X0,identity),
inference(superposition,[status(thm)],[c_7799,c_616]) ).
tcf(c_10137,plain,
! [X0: $i] : least_upper_bound(inverse(X0),least_upper_bound(X0,identity)) = least_upper_bound(inverse(X0),X0),
inference(superposition,[status(thm)],[c_8770,c_1663]) ).
tcf(c_10362,plain,
! [X0: $i] : least_upper_bound(identity,least_upper_bound(X0,inverse(X0))) = least_upper_bound(X0,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_10137,c_75,c_73,c_76,c_74]) ).
tcf(c_12058,plain,
! [X0: $i] : multiply(least_upper_bound(identity,inverse(X0)),least_upper_bound(identity,X0)) = least_upper_bound(least_upper_bound(identity,X0),least_upper_bound(identity,inverse(X0))),
inference(superposition,[status(thm)],[c_5394,c_245]) ).
tcf(c_12355,plain,
! [X0: $i] : multiply(least_upper_bound(identity,inverse(X0)),least_upper_bound(identity,X0)) = least_upper_bound(identity,least_upper_bound(X0,least_upper_bound(identity,inverse(X0)))),
inference(theory_normalisation,[status(thm)],[c_12058,c_75,c_73,c_76,c_74]) ).
tcf(c_12356,plain,
! [X0: $i] : multiply(least_upper_bound(identity,inverse(X0)),least_upper_bound(identity,X0)) = least_upper_bound(identity,least_upper_bound(X0,inverse(X0))),
inference(ac_demodulation,[status(thm)],[c_12355,c_77,c_75,c_73,c_76,c_74]) ).
tcf(c_12357,plain,
! [X0: $i] : multiply(least_upper_bound(identity,inverse(X0)),least_upper_bound(identity,X0)) = least_upper_bound(X0,inverse(X0)),
inference(demodulation,[status(thm)],[c_12356,c_10362]) ).
tcf(c_13541,plain,
$false,
inference(ground_joinability,[status(thm)],[c_7894,c_10362,c_12357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.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 14:03:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 7.43/2.21 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 7.43/2.21 % SZS status Started for theBenchmark.p
% 7.43/2.21 % SZS status Unsatisfiable for theBenchmark.p
% 7.43/2.21
% 7.43/2.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.43/2.21
% 7.43/2.21 % ------ iProver source info
% 7.43/2.21
% 7.43/2.21 % git: date: 2026-07-19 20:42:38 +0200
% 7.43/2.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.43/2.21 % git: non_committed_changes: false
% 7.43/2.21
% 7.43/2.21 % ------ Parsing...% successful
% 7.43/2.21
% 7.43/2.21
% 7.43/2.21 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.43/2.21 % ------ Proving...
% 7.43/2.21 % ------ Problem Properties
% 7.43/2.21
% 7.43/2.21 %
% 7.43/2.21 % clauses 21
% 7.43/2.21 % conjectures 1
% 7.43/2.21 % EPR 0
% 7.43/2.21 % Horn 21
% 7.43/2.21 % unary 21
% 7.43/2.21 % binary 0
% 7.43/2.21 % lits 21
% 7.43/2.21 % lits eq 21
% 7.43/2.21 % fd_pure 0
% 7.43/2.21 % fd_pseudo 0
% 7.43/2.21 % fd_cond 0
% 7.43/2.21 % fd_pseudo_cond 0
% 7.43/2.21 % AC symbols 2
% 7.43/2.21
% 7.43/2.21 % ------ Input Options Time Limit: Unbounded
% 7.43/2.21
% 7.43/2.21
% 7.43/2.21 % ------
% 7.43/2.21 % Current options:
% 7.43/2.21 % ------
% 7.43/2.21
% 7.43/2.21
% 7.43/2.21 %
% 7.43/2.21
% 7.43/2.21 % ------ Proving...
% 7.43/2.21 %
% 7.43/2.21
% 7.43/2.21 % SZS status Unsatisfiable for theBenchmark.p
% 7.43/2.21
% 7.43/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.43/2.21
% 7.43/2.21
%------------------------------------------------------------------------------