%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP169-2 : 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 : n019.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 3.21s 6.61s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 64 ( 64 unt; 0 def)
% Number of atoms : 64 ( 63 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 : 90 ( 0 sgn 90 !; 0 ?; 60 :)
% 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(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(f10,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
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,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02b_1) ).
fof(f18,plain,
inverse(a) = greatest_lower_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02b) ).
fof(f20,plain,
b != greatest_lower_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_74,plain,
! [X0: $i] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
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,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
greatest_lower_bound(a,b) != b,
inference(cnf_transformation,[],[f20]) ).
tcf(c_221,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_230,plain,
! [X0: $i,X1: $i] : least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X0,X1))) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c_75,c_221]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X0,X1))) = identity,
inference(light_normalisation,[status(thm)],[c_230,c_67]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_67,c_68]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] : least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X1,X0))) = identity,
inference(superposition,[status(thm)],[c_69,c_239]) ).
tcf(c_287,plain,
least_upper_bound(identity,multiply(inverse(inverse(b)),inverse(a))) = identity,
inference(superposition,[status(thm)],[c_81,c_276]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_70,c_76]) ).
tcf(c_464,plain,
greatest_lower_bound(multiply(inverse(inverse(b)),inverse(a)),identity) = multiply(inverse(inverse(b)),inverse(a)),
inference(superposition,[status(thm)],[c_287,c_407]) ).
tcf(c_472,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(b)),inverse(a))) = multiply(inverse(inverse(b)),inverse(a)),
inference(theory_normalisation,[status(thm)],[c_464,c_71,c_69,c_72,c_70]) ).
tcf(c_524,plain,
! [X0: $i] : greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(inverse(b)),inverse(a)),X0)) = greatest_lower_bound(multiply(inverse(inverse(b)),inverse(a)),X0),
inference(superposition,[status(thm)],[c_472,c_71]) ).
tcf(c_537,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(multiply(inverse(inverse(b)),inverse(a)),X0)) = identity,
inference(superposition,[status(thm)],[c_524,c_75]) ).
tcf(c_545,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(X0,multiply(inverse(inverse(b)),inverse(a)))) = identity,
inference(superposition,[status(thm)],[c_69,c_537]) ).
tcf(c_2489,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_266,c_66]) ).
tcf(c_2491,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_67,c_2489]) ).
tcf(c_2494,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_2489,c_2489]) ).
tcf(c_2518,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(X0,multiply(b,inverse(a)))) = identity,
inference(demodulation,[status(thm)],[c_545,c_2494]) ).
tcf(c_2619,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_2491,c_2494]) ).
tcf(c_2750,plain,
! [X0: $i] : least_upper_bound(identity,multiply(greatest_lower_bound(X0,b),inverse(a))) = identity,
inference(superposition,[status(thm)],[c_80,c_2518]) ).
tcf(c_3095,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_2494,c_67]) ).
tcf(c_3101,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_2494,c_2619]) ).
tcf(c_3102,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3101,c_2619]) ).
tcf(c_3142,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(X0,X1),inverse(X0)) = least_upper_bound(identity,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_3095,c_79]) ).
tcf(c_3162,plain,
! [X0: $i] : multiply(least_upper_bound(a,greatest_lower_bound(X0,b)),inverse(a)) = identity,
inference(demodulation,[status(thm)],[c_2750,c_3142]) ).
tcf(c_3346,plain,
! [X0: $i] : multiply(inverse(least_upper_bound(a,greatest_lower_bound(X0,b))),identity) = inverse(a),
inference(superposition,[status(thm)],[c_3162,c_2489]) ).
tcf(c_3416,plain,
! [X0: $i] : inverse(least_upper_bound(a,greatest_lower_bound(X0,b))) = inverse(a),
inference(demodulation,[status(thm)],[c_3346,c_2619]) ).
tcf(c_3420,plain,
inverse(least_upper_bound(a,b)) = inverse(a),
inference(superposition,[status(thm)],[c_74,c_3416]) ).
tcf(c_3558,plain,
inverse(inverse(a)) = least_upper_bound(a,b),
inference(superposition,[status(thm)],[c_3420,c_3102]) ).
tcf(c_3572,plain,
least_upper_bound(a,b) = a,
inference(demodulation,[status(thm)],[c_3558,c_3102]) ).
tcf(c_3578,plain,
greatest_lower_bound(b,a) = b,
inference(superposition,[status(thm)],[c_3572,c_407]) ).
tcf(c_3582,plain,
greatest_lower_bound(a,b) = b,
inference(theory_normalisation,[status(thm)],[c_3578,c_71,c_69,c_72,c_70]) ).
tcf(c_3583,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3582,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.62 % Computer : n019.cluster.edu
% 0.13/5.62 % Model : x86_64 x86_64
% 0.13/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.62 % Memory : 8046.5625MB
% 0.13/5.62 % OS : Linux 6.8.0-71-generic
% 0.13/5.62 % CPULimit : 300
% 0.13/5.62 % WCLimit : 300
% 0.13/5.62 % DateTime : Wed Sep 23 13:57:29 UTC 2026
% 0.13/5.62 % CPUTime :
% 0.13/5.62 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.67 Running UEQ theorem proving
% 0.13/5.67 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
% 0.13/5.69
% 0.13/5.69 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.69
% 0.13/5.69 % Detected problem language: tptp
% 0.17/5.71 % Proving...
% 3.21/6.61 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.21/6.61 % SZS status Started for theBenchmark.p
% 3.21/6.61 % SZS status Unsatisfiable for theBenchmark.p
% 3.21/6.61
% 3.21/6.61 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.21/6.61
% 3.21/6.61 % ------ iProver source info
% 3.21/6.61
% 3.21/6.61 % git: date: 2026-07-19 20:42:38 +0200
% 3.21/6.61 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.21/6.61 % git: non_committed_changes: false
% 3.21/6.61
% 3.21/6.61 % ------ Parsing...% successful
% 3.21/6.61
% 3.21/6.61
% 3.21/6.61 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.21/6.61
% 3.21/6.61 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.21/6.61
% 3.21/6.61 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.21/6.61
% 3.21/6.61 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.21/6.61 % ------ Proving...
% 3.21/6.61 % ------ Problem Properties
% 3.21/6.61
% 3.21/6.61 %
% 3.21/6.61 % clauses 17
% 3.21/6.61 % conjectures 1
% 3.21/6.61 % EPR 0
% 3.21/6.61 % Horn 17
% 3.21/6.61 % unary 17
% 3.21/6.61 % binary 0
% 3.21/6.61 % lits 17
% 3.21/6.61 % lits eq 17
% 3.21/6.61 % fd_pure 0
% 3.21/6.61 % fd_pseudo 0
% 3.21/6.61 % fd_cond 0
% 3.21/6.61 % fd_pseudo_cond 0
% 3.21/6.61 % AC symbols 2
% 3.21/6.61
% 3.21/6.61 % ------ Input Options Time Limit: Unbounded
% 3.21/6.61
% 3.21/6.61
% 3.21/6.61 % ------
% 3.21/6.61 % Current options:
% 3.21/6.61 % ------
% 3.21/6.61
% 3.21/6.61
% 3.21/6.61 %
% 3.21/6.61
% 3.21/6.61 % ------ Proving...
% 3.21/6.61 %
% 3.21/6.61
% 3.21/6.61 % SZS status Unsatisfiable for theBenchmark.p
% 3.21/6.61
% 3.21/6.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.21/6.62
% 3.21/6.62
%------------------------------------------------------------------------------