%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP184-2 : 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 : n006.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 01:31:43 PM UTC 2026
% Result : Unsatisfiable 20.52s 4.67s
% Output : CNFRefutation 20.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 82 ( 0 sgn 82 !; 0 ?; 54 :)
% 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(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(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
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',p21_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',p21_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_3) ).
fof(f21,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_p21) ).
tcf(c_68,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,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_74,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_79,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_80,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_81,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_82,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_83,plain,
inverse(identity) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_86,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,[],[f21]) ).
tcf(c_116,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_86,c_74,c_72,c_73,c_71]) ).
tcf(c_118,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_84,c_69]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_130,plain,
! [X0: $i] : inverse(multiply(identity,X0)) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[c_83,c_85]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] : least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_68,c_81]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_68,c_82]) ).
tcf(c_250,plain,
! [X0: $i] : multiply(inverse(X0),identity) = inverse(X0),
inference(demodulation,[status(thm)],[c_130,c_68]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(theory_normalisation,[status(thm)],[c_215,c_74,c_72,c_73,c_71]) ).
tcf(c_557,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_84,c_250]) ).
tcf(c_1255,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
inference(superposition,[status(thm)],[c_557,c_80]) ).
tcf(c_1256,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
inference(superposition,[status(thm)],[c_557,c_79]) ).
tcf(c_1447,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),inverse(X0)) = greatest_lower_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_118,c_231]) ).
tcf(c_1529,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,X0),inverse(X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_1447,c_74,c_72,c_73,c_71]) ).
tcf(c_2112,plain,
! [X0: $i] : multiply(X0,inverse(greatest_lower_bound(identity,X0))) = inverse(greatest_lower_bound(identity,inverse(X0))),
inference(superposition,[status(thm)],[c_1529,c_129]) ).
tcf(c_3828,plain,
! [X0: $i] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_69,c_1255]) ).
tcf(c_3907,plain,
! [X0: $i] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_3828,c_74,c_72,c_73,c_71]) ).
tcf(c_8842,plain,
! [X0: $i] : multiply(inverse(greatest_lower_bound(identity,X0)),X0) = inverse(greatest_lower_bound(identity,inverse(X0))),
inference(superposition,[status(thm)],[c_3907,c_131]) ).
tcf(c_22211,plain,
! [X0: $i] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = multiply(least_upper_bound(X0,identity),inverse(greatest_lower_bound(identity,X0))),
inference(superposition,[status(thm)],[c_2112,c_254]) ).
tcf(c_40407,plain,
! [X0: $i] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),inverse(greatest_lower_bound(identity,inverse(X0)))) = multiply(inverse(greatest_lower_bound(identity,X0)),least_upper_bound(identity,X0)),
inference(superposition,[status(thm)],[c_8842,c_1256]) ).
tcf(c_40612,plain,
! [X0: $i] : multiply(inverse(greatest_lower_bound(identity,X0)),least_upper_bound(identity,X0)) = multiply(least_upper_bound(X0,identity),inverse(greatest_lower_bound(identity,X0))),
inference(demodulation,[status(thm)],[c_40407,c_22211]) ).
tcf(c_40703,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(identity,a))),
inference(demodulation,[status(thm)],[c_116,c_40612]) ).
tcf(c_40704,plain,
$false,
inference(theory_normalisation,[status(thm)],[c_40703,c_74,c_72,c_73,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.81 % Computer : n006.cluster.edu
% 0.09/0.81 % Model : x86_64 x86_64
% 0.09/0.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.81 % Memory : 8046.5625MB
% 0.09/0.81 % OS : Linux 6.8.0-71-generic
% 0.09/0.81 % CPULimit : 300
% 0.09/0.81 % WCLimit : 300
% 0.09/0.81 % DateTime : Wed Sep 23 14:02:45 UTC 2026
% 0.09/0.81 % CPUTime :
% 0.09/0.81 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.85 Running UEQ theorem proving
% 0.09/0.85 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
% 0.09/0.86
% 0.09/0.86 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.86
% 0.09/0.86 % Detected problem language: tptp
% 0.09/0.87 % Proving...
% 20.52/4.67 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 20.52/4.67 % SZS status Started for theBenchmark.p
% 20.52/4.67 % SZS status Unsatisfiable for theBenchmark.p
% 20.52/4.67
% 20.52/4.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.52/4.67
% 20.52/4.67 % ------ iProver source info
% 20.52/4.67
% 20.52/4.67 % git: date: 2026-07-19 20:42:38 +0200
% 20.52/4.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.52/4.67 % git: non_committed_changes: false
% 20.52/4.67
% 20.52/4.67 % ------ Parsing...% successful
% 20.52/4.67
% 20.52/4.67
% 20.52/4.67 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.52/4.67 % ------ Proving...
% 20.52/4.67 % ------ Problem Properties
% 20.52/4.67
% 20.52/4.67 %
% 20.52/4.67 % clauses 19
% 20.52/4.67 % conjectures 1
% 20.52/4.67 % EPR 0
% 20.52/4.67 % Horn 19
% 20.52/4.67 % unary 19
% 20.52/4.67 % binary 0
% 20.52/4.67 % lits 19
% 20.52/4.67 % lits eq 19
% 20.52/4.67 % fd_pure 0
% 20.52/4.67 % fd_pseudo 0
% 20.52/4.67 % fd_cond 0
% 20.52/4.67 % fd_pseudo_cond 0
% 20.52/4.67 % AC symbols 2
% 20.52/4.67
% 20.52/4.67 % ------ Input Options Time Limit: Unbounded
% 20.52/4.67
% 20.52/4.67
% 20.52/4.67 % ------
% 20.52/4.67 % Current options:
% 20.52/4.67 % ------
% 20.52/4.67
% 20.52/4.67
% 20.52/4.67 %
% 20.52/4.67
% 20.52/4.67 % ------ Proving...
% 20.52/4.67 %
% 20.52/4.67
% 20.52/4.67 % SZS status Unsatisfiable for theBenchmark.p
% 20.52/4.67
% 20.52/4.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.52/4.68
% 20.52/4.68
%------------------------------------------------------------------------------