%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP169-1 : 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 : n005.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 01:31:38 PM UTC 2026
% Result : Unsatisfiable 2.99s 1.22s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 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(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/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(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,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p02a_1) ).
fof(f18,plain,
inverse(b) = least_upper_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(a,b) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p02a) ).
fof(f20,plain,
a != least_upper_bound(a,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_75,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
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_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,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
least_upper_bound(a,b) != a,
inference(cnf_transformation,[],[f20]) ).
tcf(c_222,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_231,plain,
least_upper_bound(identity,multiply(inverse(inverse(a)),inverse(b))) = multiply(inverse(inverse(a)),inverse(b)),
inference(superposition,[status(thm)],[c_81,c_222]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_69,c_75]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_67,c_68]) ).
tcf(c_275,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(a)),inverse(b))) = identity,
inference(superposition,[status(thm)],[c_231,c_76]) ).
tcf(c_399,plain,
! [X0: $i] : greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(inverse(a)),inverse(b)),X0)) = greatest_lower_bound(identity,X0),
inference(superposition,[status(thm)],[c_275,c_71]) ).
tcf(c_404,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_71,c_256]) ).
tcf(c_441,plain,
! [X0: $i] : greatest_lower_bound(identity,least_upper_bound(multiply(inverse(inverse(a)),inverse(b)),X0)) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),inverse(b))),
inference(superposition,[status(thm)],[c_76,c_399]) ).
tcf(c_450,plain,
! [X0: $i] : greatest_lower_bound(identity,least_upper_bound(multiply(inverse(inverse(a)),inverse(b)),X0)) = identity,
inference(light_normalisation,[status(thm)],[c_441,c_275]) ).
tcf(c_1941,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_267,c_66]) ).
tcf(c_1943,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_67,c_1941]) ).
tcf(c_1946,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_1941,c_1941]) ).
tcf(c_1962,plain,
! [X0: $i] : greatest_lower_bound(identity,least_upper_bound(multiply(a,inverse(b)),X0)) = identity,
inference(demodulation,[status(thm)],[c_450,c_1946]) ).
tcf(c_2133,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(least_upper_bound(a,X0),inverse(b))) = identity,
inference(superposition,[status(thm)],[c_79,c_1962]) ).
tcf(c_2409,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_1943,c_1946]) ).
tcf(c_2897,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_1946,c_67]) ).
tcf(c_2904,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_1946,c_2409]) ).
tcf(c_2905,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2904,c_2409]) ).
tcf(c_2943,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,X1),inverse(X0)) = greatest_lower_bound(identity,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_2897,c_80]) ).
tcf(c_2963,plain,
! [X0: $i] : multiply(greatest_lower_bound(b,least_upper_bound(a,X0)),inverse(b)) = identity,
inference(demodulation,[status(thm)],[c_2133,c_2943]) ).
tcf(c_3227,plain,
! [X0: $i] : multiply(inverse(greatest_lower_bound(b,least_upper_bound(a,X0))),identity) = inverse(b),
inference(superposition,[status(thm)],[c_2963,c_1941]) ).
tcf(c_3273,plain,
! [X0: $i] : inverse(greatest_lower_bound(b,least_upper_bound(a,X0))) = inverse(b),
inference(demodulation,[status(thm)],[c_3227,c_2409]) ).
tcf(c_3283,plain,
inverse(greatest_lower_bound(b,a)) = inverse(b),
inference(superposition,[status(thm)],[c_404,c_3273]) ).
tcf(c_3295,plain,
inverse(greatest_lower_bound(a,b)) = inverse(b),
inference(theory_normalisation,[status(thm)],[c_3283,c_72,c_70,c_71,c_69]) ).
tcf(c_3461,plain,
inverse(inverse(b)) = greatest_lower_bound(a,b),
inference(superposition,[status(thm)],[c_3295,c_2905]) ).
tcf(c_3476,plain,
greatest_lower_bound(a,b) = b,
inference(demodulation,[status(thm)],[c_3461,c_2905]) ).
tcf(c_3481,plain,
least_upper_bound(a,b) = a,
inference(superposition,[status(thm)],[c_3476,c_75]) ).
tcf(c_3486,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3481,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Wed Sep 23 13:56:49 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running UEQ theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 2.99/1.22 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.99/1.22 % SZS status Started for theBenchmark.p
% 2.99/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 2.99/1.22
% 2.99/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.99/1.22
% 2.99/1.22 % ------ iProver source info
% 2.99/1.22
% 2.99/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 2.99/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.99/1.22 % git: non_committed_changes: false
% 2.99/1.22
% 2.99/1.22 % ------ Parsing...% successful
% 2.99/1.22
% 2.99/1.22
% 2.99/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.99/1.22
% 2.99/1.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.99/1.22
% 2.99/1.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.99/1.22
% 2.99/1.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.99/1.22 % ------ Proving...
% 2.99/1.22 % ------ Problem Properties
% 2.99/1.22
% 2.99/1.22 %
% 2.99/1.22 % clauses 17
% 2.99/1.22 % conjectures 1
% 2.99/1.22 % EPR 0
% 2.99/1.22 % Horn 17
% 2.99/1.22 % unary 17
% 2.99/1.22 % binary 0
% 2.99/1.22 % lits 17
% 2.99/1.22 % lits eq 17
% 2.99/1.22 % fd_pure 0
% 2.99/1.22 % fd_pseudo 0
% 2.99/1.22 % fd_cond 0
% 2.99/1.22 % fd_pseudo_cond 0
% 2.99/1.22 % AC symbols 2
% 2.99/1.22
% 2.99/1.22 % ------ Input Options Time Limit: Unbounded
% 2.99/1.22
% 2.99/1.22
% 2.99/1.22 % ------
% 2.99/1.22 % Current options:
% 2.99/1.22 % ------
% 2.99/1.22
% 2.99/1.22
% 2.99/1.22 %
% 2.99/1.22
% 2.99/1.22 % ------ Proving...
% 2.99/1.22 %
% 2.99/1.22
% 2.99/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 2.99/1.22
% 2.99/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.99/1.22
% 2.99/1.22
%------------------------------------------------------------------------------