%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP170-2 : 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 : n008.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 01:31:39 PM UTC 2026
% Result : Unsatisfiable 26.62s 4.74s
% Output : CNFRefutation 26.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 77 ( 77 unt; 3 def)
% Number of atoms : 129 ( 76 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?; 61 :)
% 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(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(f17,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03b_1) ).
fof(f18,plain,
a = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03b_2) ).
fof(f20,plain,
c = greatest_lower_bound(c,d),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p03b) ).
fof(f22,plain,
multiply(a,c) != greatest_lower_bound(multiply(a,c),multiply(b,d)),
inference(reorient_equations,[],[f21]) ).
tcf(c_67,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_72,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_73,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_76,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,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] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_82,plain,
greatest_lower_bound(a,b) = a,
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,plain,
greatest_lower_bound(c,d) = c,
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
inference(cnf_transformation,[],[f22]) ).
tcf(c_141,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_142,definition,
iPr_def_11 = multiply(b,d),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_143,definition,
iPr_def_12 = greatest_lower_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_144,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_84,c_142,c_141,c_143]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_70,c_76]) ).
tcf(c_237,plain,
least_upper_bound(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_143,c_76]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_71,c_77]) ).
tcf(c_262,plain,
least_upper_bound(b,a) = b,
inference(superposition,[status(thm)],[c_82,c_234]) ).
tcf(c_263,plain,
least_upper_bound(d,c) = d,
inference(superposition,[status(thm)],[c_83,c_234]) ).
tcf(c_270,plain,
least_upper_bound(c,d) = d,
inference(demodulation,[status(thm)],[c_263,c_71]) ).
tcf(c_271,plain,
least_upper_bound(a,b) = b,
inference(demodulation,[status(thm)],[c_262,c_71]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_288,c_67]) ).
tcf(c_349,plain,
multiply(inverse(a),iPr_def_10) = c,
inference(superposition,[status(thm)],[c_141,c_289]) ).
tcf(c_350,plain,
multiply(inverse(b),iPr_def_11) = d,
inference(superposition,[status(thm)],[c_142,c_289]) ).
tcf(c_352,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_68,c_289]) ).
tcf(c_360,plain,
multiply(inverse(inverse(a)),c) = iPr_def_10,
inference(superposition,[status(thm)],[c_349,c_289]) ).
tcf(c_365,plain,
multiply(inverse(inverse(b)),d) = iPr_def_11,
inference(superposition,[status(thm)],[c_350,c_289]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2),
inference(superposition,[status(thm)],[c_77,c_72]) ).
tcf(c_410,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(iPr_def_11,X0)) = greatest_lower_bound(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_143,c_72]) ).
tcf(c_422,plain,
! [X0: $i] : multiply(inverse(inverse(inverse(X0))),X0) = identity,
inference(superposition,[status(thm)],[c_352,c_289]) ).
tcf(c_474,plain,
! [X0: $i] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[status(thm)],[c_422,c_289]) ).
tcf(c_477,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_474,c_352]) ).
tcf(c_479,plain,
multiply(a,c) = iPr_def_10,
inference(demodulation,[status(thm)],[c_360,c_477]) ).
tcf(c_480,plain,
multiply(b,d) = iPr_def_11,
inference(demodulation,[status(thm)],[c_365,c_477]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_477,c_289]) ).
tcf(c_525,plain,
! [X0: $i] : least_upper_bound(c,least_upper_bound(d,X0)) = least_upper_bound(d,X0),
inference(superposition,[status(thm)],[c_270,c_73]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_73,c_244]) ).
tcf(c_731,plain,
! [X0: $i] : multiply(a,least_upper_bound(c,X0)) = least_upper_bound(iPr_def_10,multiply(a,X0)),
inference(superposition,[status(thm)],[c_479,c_78]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,least_upper_bound(multiply(inverse(X0),X1),X2)) = least_upper_bound(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[c_487,c_78]) ).
tcf(c_1251,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(X0,iPr_def_11)) = greatest_lower_bound(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_70,c_410]) ).
tcf(c_2164,plain,
! [X0: $i] : least_upper_bound(c,least_upper_bound(X0,d)) = least_upper_bound(X0,d),
inference(superposition,[status(thm)],[c_71,c_525]) ).
tcf(c_2483,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_12,least_upper_bound(X0,iPr_def_10)) = iPr_def_12,
inference(superposition,[status(thm)],[c_237,c_528]) ).
tcf(c_2552,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_12,least_upper_bound(iPr_def_10,X0)) = iPr_def_12,
inference(superposition,[status(thm)],[c_71,c_2483]) ).
tcf(c_8460,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_12,least_upper_bound(iPr_def_10,X0)) = greatest_lower_bound(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_408,c_1251]) ).
tcf(c_8475,plain,
greatest_lower_bound(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_8460,c_2552]) ).
tcf(c_12478,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,multiply(a,least_upper_bound(c,X0))) = iPr_def_10,
inference(superposition,[status(thm)],[c_731,c_77]) ).
tcf(c_12623,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,multiply(a,least_upper_bound(X0,d))) = iPr_def_10,
inference(superposition,[status(thm)],[c_2164,c_12478]) ).
tcf(c_20818,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,least_upper_bound(X0,multiply(a,d))) = iPr_def_10,
inference(superposition,[status(thm)],[c_744,c_12623]) ).
tcf(c_21032,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,least_upper_bound(multiply(a,d),X0)) = iPr_def_10,
inference(superposition,[status(thm)],[c_71,c_20818]) ).
tcf(c_21146,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,multiply(least_upper_bound(a,X0),d)) = iPr_def_10,
inference(superposition,[status(thm)],[c_80,c_21032]) ).
tcf(c_21274,plain,
greatest_lower_bound(iPr_def_10,multiply(b,d)) = iPr_def_10,
inference(superposition,[status(thm)],[c_271,c_21146]) ).
tcf(c_21301,plain,
iPr_def_10 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_21274,c_480,c_8475]) ).
tcf(c_21367,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_144,c_21301]) ).
tcf(c_21368,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_21367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 13:57:59 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running UEQ theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 26.62/4.74 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 26.62/4.74 % SZS status Started for theBenchmark.p
% 26.62/4.74 % SZS status Unsatisfiable for theBenchmark.p
% 26.62/4.74
% 26.62/4.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.62/4.74
% 26.62/4.74 % ------ iProver source info
% 26.62/4.74
% 26.62/4.74 % git: date: 2026-07-19 20:42:38 +0200
% 26.62/4.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.62/4.74 % git: non_committed_changes: false
% 26.62/4.74
% 26.62/4.74 % ------ Parsing...% successful
% 26.62/4.74
% 26.62/4.74
% 26.62/4.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.62/4.74
% 26.62/4.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 26.62/4.74
% 26.62/4.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.62/4.74
% 26.62/4.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 26.62/4.74 % ------ Proving...
% 26.62/4.74 % ------ Problem Properties
% 26.62/4.74
% 26.62/4.74 %
% 26.62/4.74 % clauses 21
% 26.62/4.74 % conjectures 1
% 26.62/4.74 % EPR 1
% 26.62/4.74 % Horn 21
% 26.62/4.74 % unary 21
% 26.62/4.74 % binary 0
% 26.62/4.74 % lits 21
% 26.62/4.74 % lits eq 21
% 26.62/4.74 % fd_pure 0
% 26.62/4.74 % fd_pseudo 0
% 26.62/4.74 % fd_cond 0
% 26.62/4.74 % fd_pseudo_cond 0
% 26.62/4.74 % AC symbols 2
% 26.62/4.74
% 26.62/4.74 % ------ Input Options Time Limit: Unbounded
% 26.62/4.74
% 26.62/4.74
% 26.62/4.74 % ------
% 26.62/4.74 % Current options:
% 26.62/4.74 % ------
% 26.62/4.74
% 26.62/4.74
% 26.62/4.74 %
% 26.62/4.74
% 26.62/4.74 % ------ Proving...
% 26.62/4.74 %
% 26.62/4.74
% 26.62/4.74 % SZS status Unsatisfiable for theBenchmark.p
% 26.62/4.74
% 26.62/4.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.62/4.74
% 26.62/4.74
%------------------------------------------------------------------------------