%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP185-4 : 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 : n014.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 8.30s 1.73s
% Output : CNFRefutation 8.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 87 ( 87 unt; 7 def)
% Number of atoms : 168 ( 86 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 : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?; 77 :)
% 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(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(f17,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22b_1) ).
fof(f18,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22b_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22b_3) ).
fof(f21,negated_conjecture,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22b) ).
fof(f22,plain,
least_upper_bound(multiply(a,b),identity) != greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(reorient_equations,[],[f21]) ).
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_70,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
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_78,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
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_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_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,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(cnf_transformation,[],[f22]) ).
tcf(c_148,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_149,definition,
iPr_def_11 = least_upper_bound(iPr_def_10,identity),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_150,definition,
iPr_def_12 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_151,definition,
iPr_def_13 = least_upper_bound(b,identity),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_152,definition,
iPr_def_14 = multiply(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_153,definition,
iPr_def_15 = greatest_lower_bound(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_154,definition,
iPr_def_16 = inverse(identity),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_155,negated_conjecture,
iPr_def_15 != iPr_def_11,
inference(demodulation,[status(thm)],[c_86,c_151,c_150,c_152,c_148,c_149,c_153]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_157,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_158,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_167,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_74]) ).
tcf(c_168,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_73]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_172,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_173,plain,
iPr_def_16 = identity,
inference(demodulation,[status(thm)],[c_83,c_154]) ).
tcf(c_265,plain,
inverse(iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_154,c_173]) ).
tcf(c_266,plain,
! [X0: $i] : multiply(iPr_def_16,X0) = X0,
inference(demodulation,[status(thm)],[c_158,c_173]) ).
tcf(c_267,plain,
least_upper_bound(iPr_def_10,iPr_def_16) = iPr_def_11,
inference(demodulation,[status(thm)],[c_149,c_173]) ).
tcf(c_268,plain,
least_upper_bound(a,iPr_def_16) = iPr_def_12,
inference(demodulation,[status(thm)],[c_150,c_173]) ).
tcf(c_269,plain,
least_upper_bound(iPr_def_16,a) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_268,c_167,c_169,c_168,c_170]) ).
tcf(c_270,plain,
least_upper_bound(b,iPr_def_16) = iPr_def_13,
inference(demodulation,[status(thm)],[c_151,c_173]) ).
tcf(c_271,plain,
least_upper_bound(iPr_def_16,b) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_270,c_167,c_169,c_168,c_170]) ).
tcf(c_272,plain,
greatest_lower_bound(iPr_def_14,iPr_def_11) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_153,c_167,c_169,c_168,c_170]) ).
tcf(c_273,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_16,
inference(demodulation,[status(thm)],[c_157,c_173]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
inference(superposition,[status(thm)],[c_167,c_169]) ).
tcf(c_309,plain,
! [X0: $i] : inverse(multiply(iPr_def_16,X0)) = multiply(inverse(X0),iPr_def_16),
inference(superposition,[status(thm)],[c_265,c_171]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(iPr_def_16,X1),
inference(superposition,[status(thm)],[c_273,c_156]) ).
tcf(c_320,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,least_upper_bound(iPr_def_16,X0)) = least_upper_bound(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_267,c_167]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_274,c_163]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(iPr_def_16,X1),X0),
inference(superposition,[status(thm)],[c_266,c_160]) ).
tcf(c_495,plain,
! [X0: $i] : multiply(inverse(X0),iPr_def_16) = inverse(X0),
inference(demodulation,[status(thm)],[c_309,c_266]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_313,c_266]) ).
tcf(c_848,plain,
! [X0: $i] : multiply(X0,iPr_def_16) = X0,
inference(superposition,[status(thm)],[c_172,c_495]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_172,c_497]) ).
tcf(c_872,plain,
multiply(inverse(a),iPr_def_10) = b,
inference(superposition,[status(thm)],[c_148,c_497]) ).
tcf(c_875,plain,
multiply(inverse(iPr_def_12),iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_152,c_497]) ).
tcf(c_936,plain,
least_upper_bound(iPr_def_10,iPr_def_12) = least_upper_bound(iPr_def_11,a),
inference(superposition,[status(thm)],[c_269,c_320]) ).
tcf(c_1045,plain,
least_upper_bound(iPr_def_11,a) = least_upper_bound(iPr_def_12,iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_936,c_167,c_169,c_168,c_170]) ).
tcf(c_1537,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(iPr_def_16,X1)),
inference(superposition,[status(thm)],[c_848,c_162]) ).
tcf(c_2239,plain,
multiply(a,b) = iPr_def_10,
inference(superposition,[status(thm)],[c_872,c_868]) ).
tcf(c_2240,plain,
multiply(iPr_def_12,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_875,c_868]) ).
tcf(c_2425,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(X0,least_upper_bound(iPr_def_12,iPr_def_10))) = iPr_def_11,
inference(superposition,[status(thm)],[c_1045,c_378]) ).
tcf(c_6995,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(least_upper_bound(iPr_def_12,iPr_def_10),X0)) = iPr_def_11,
inference(superposition,[status(thm)],[c_169,c_2425]) ).
tcf(c_7136,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(iPr_def_12,least_upper_bound(iPr_def_10,X0))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_6995,c_167,c_169,c_168,c_170]) ).
tcf(c_9548,plain,
multiply(least_upper_bound(iPr_def_16,a),b) = least_upper_bound(b,iPr_def_10),
inference(superposition,[status(thm)],[c_2239,c_412]) ).
tcf(c_9639,plain,
multiply(least_upper_bound(iPr_def_16,a),b) = least_upper_bound(iPr_def_10,b),
inference(theory_normalisation,[status(thm)],[c_9548,c_167,c_169,c_168,c_170]) ).
tcf(c_9640,plain,
multiply(iPr_def_12,b) = least_upper_bound(iPr_def_10,b),
inference(demodulation,[status(thm)],[c_9639,c_269]) ).
tcf(c_9904,plain,
greatest_lower_bound(iPr_def_11,least_upper_bound(iPr_def_12,multiply(iPr_def_12,b))) = iPr_def_11,
inference(superposition,[status(thm)],[c_9640,c_7136]) ).
tcf(c_10077,plain,
iPr_def_11 = iPr_def_15,
inference(demodulation,[status(thm)],[c_9904,c_170,c_271,c_272,c_1537,c_2240]) ).
tcf(c_10246,plain,
$false,
inference(superposition,[status(thm)],[c_10077,c_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 14:03:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running UEQ theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 8.30/1.73 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.30/1.73 % SZS status Started for theBenchmark.p
% 8.30/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.30/1.73
% 8.30/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.30/1.73
% 8.30/1.73 % ------ iProver source info
% 8.30/1.73
% 8.30/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 8.30/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.30/1.73 % git: non_committed_changes: false
% 8.30/1.73
% 8.30/1.73 % ------ Parsing...% successful
% 8.30/1.73
% 8.30/1.73
% 8.30/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.30/1.73
% 8.30/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.30/1.73
% 8.30/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.30/1.73
% 8.30/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.30/1.73 % ------ Proving...
% 8.30/1.73 % ------ Problem Properties
% 8.30/1.73
% 8.30/1.73 %
% 8.30/1.73 % clauses 26
% 8.30/1.73 % conjectures 1
% 8.30/1.73 % EPR 2
% 8.30/1.73 % Horn 26
% 8.30/1.73 % unary 26
% 8.30/1.73 % binary 0
% 8.30/1.73 % lits 26
% 8.30/1.73 % lits eq 26
% 8.30/1.73 % fd_pure 0
% 8.30/1.73 % fd_pseudo 0
% 8.30/1.73 % fd_cond 0
% 8.30/1.73 % fd_pseudo_cond 0
% 8.30/1.73 % AC symbols 2
% 8.30/1.73
% 8.30/1.73 % ------ Input Options Time Limit: Unbounded
% 8.30/1.73
% 8.30/1.73
% 8.30/1.73 % ------
% 8.30/1.73 % Current options:
% 8.30/1.73 % ------
% 8.30/1.73
% 8.30/1.73
% 8.30/1.73 %
% 8.30/1.73
% 8.30/1.73 % ------ Proving...
% 8.30/1.73 %
% 8.30/1.73
% 8.30/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.30/1.73
% 8.30/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.30/1.73
% 8.30/1.73
%------------------------------------------------------------------------------