%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP172-2 : 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 : 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 01:31:39 PM UTC 2026
% Result : Unsatisfiable 3.96s 1.27s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 61 unt; 4 def)
% Number of atoms : 105 ( 60 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 : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
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(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,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04d_1) ).
fof(f18,plain,
identity = greatest_lower_bound(identity,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04d_2) ).
fof(f20,plain,
identity = greatest_lower_bound(identity,b),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p04d) ).
fof(f22,plain,
multiply(a,b) != least_upper_bound(identity,multiply(a,b)),
inference(reorient_equations,[],[f21]) ).
tcf(c_67,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
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_81,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_82,plain,
greatest_lower_bound(identity,a) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,plain,
greatest_lower_bound(identity,b) = identity,
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
inference(cnf_transformation,[],[f22]) ).
tcf(c_100,plain,
greatest_lower_bound(a,identity) = identity,
inference(theory_normalisation,[status(thm)],[c_82,c_73,c_71,c_72,c_70]) ).
tcf(c_142,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_143,definition,
iPr_def_11 = least_upper_bound(identity,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_144,definition,
iPr_def_12 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_145,definition,
iPr_def_13 = greatest_lower_bound(identity,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_146,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_84,c_142,c_143]) ).
tcf(c_147,plain,
iPr_def_12 = identity,
inference(demodulation,[status(thm)],[c_100,c_144]) ).
tcf(c_150,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_160,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_72]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_163,plain,
iPr_def_13 = identity,
inference(demodulation,[status(thm)],[c_83,c_145]) ).
tcf(c_247,plain,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_147,c_163]) ).
tcf(c_248,plain,
least_upper_bound(iPr_def_13,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_163,c_143]) ).
tcf(c_249,plain,
greatest_lower_bound(a,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_144,c_247]) ).
tcf(c_250,plain,
greatest_lower_bound(a,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_163,c_249]) ).
tcf(c_251,plain,
greatest_lower_bound(iPr_def_13,a) = iPr_def_13,
inference(demodulation,[status(thm)],[c_250,c_162]) ).
tcf(c_252,plain,
greatest_lower_bound(iPr_def_13,b) = iPr_def_13,
inference(superposition,[status(thm)],[c_163,c_145]) ).
tcf(c_258,plain,
! [X0: $i] : multiply(iPr_def_13,X0) = X0,
inference(superposition,[status(thm)],[c_163,c_150]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_161,c_155]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_162,c_156]) ).
tcf(c_280,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,multiply(X0,b)) = multiply(greatest_lower_bound(a,X0),b),
inference(superposition,[status(thm)],[c_142,c_151]) ).
tcf(c_416,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_13,greatest_lower_bound(b,X0)) = greatest_lower_bound(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_252,c_160]) ).
tcf(c_734,plain,
multiply(greatest_lower_bound(a,iPr_def_13),b) = greatest_lower_bound(iPr_def_10,b),
inference(superposition,[status(thm)],[c_258,c_280]) ).
tcf(c_741,plain,
greatest_lower_bound(iPr_def_10,b) = b,
inference(demodulation,[status(thm)],[c_734,c_162,c_251,c_258]) ).
tcf(c_1257,plain,
least_upper_bound(iPr_def_10,b) = iPr_def_10,
inference(superposition,[status(thm)],[c_741,c_156]) ).
tcf(c_1688,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_13,least_upper_bound(X0,b)) = greatest_lower_bound(iPr_def_13,b),
inference(superposition,[status(thm)],[c_272,c_416]) ).
tcf(c_1698,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_13,least_upper_bound(X0,b)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1688,c_252]) ).
tcf(c_2007,plain,
greatest_lower_bound(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_1257,c_1698]) ).
tcf(c_2044,plain,
least_upper_bound(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(superposition,[status(thm)],[c_2007,c_275]) ).
tcf(c_2048,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_2044,c_161,c_248]) ).
tcf(c_2062,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_146,c_2048]) ).
tcf(c_2063,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 13:58:20 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.44 Running UEQ theorem proving
% 0.13/0.44 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
% 0.13/0.46
% 0.13/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.46
% 0.13/0.46 % Detected problem language: tptp
% 0.13/0.48 % Proving...
% 3.96/1.27 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.96/1.27 % SZS status Started for theBenchmark.p
% 3.96/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.96/1.27
% 3.96/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.96/1.27
% 3.96/1.27 % ------ iProver source info
% 3.96/1.27
% 3.96/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.96/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.96/1.27 % git: non_committed_changes: false
% 3.96/1.27
% 3.96/1.27 % ------ Parsing...% successful
% 3.96/1.27
% 3.96/1.27
% 3.96/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.96/1.27
% 3.96/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.96/1.27
% 3.96/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.96/1.27
% 3.96/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.96/1.27 % ------ Proving...
% 3.96/1.27 % ------ Problem Properties
% 3.96/1.27
% 3.96/1.27 %
% 3.96/1.27 % clauses 22
% 3.96/1.27 % conjectures 1
% 3.96/1.27 % EPR 3
% 3.96/1.27 % Horn 22
% 3.96/1.27 % unary 22
% 3.96/1.27 % binary 0
% 3.96/1.27 % lits 22
% 3.96/1.27 % lits eq 22
% 3.96/1.27 % fd_pure 0
% 3.96/1.27 % fd_pseudo 0
% 3.96/1.27 % fd_cond 0
% 3.96/1.27 % fd_pseudo_cond 0
% 3.96/1.27 % AC symbols 2
% 3.96/1.27
% 3.96/1.27 % ------ Input Options Time Limit: Unbounded
% 3.96/1.27
% 3.96/1.27
% 3.96/1.27 % ------
% 3.96/1.27 % Current options:
% 3.96/1.27 % ------
% 3.96/1.27
% 3.96/1.27
% 3.96/1.27 %
% 3.96/1.27
% 3.96/1.27 % ------ Proving...
% 3.96/1.27 %
% 3.96/1.27
% 3.96/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.96/1.27
% 3.96/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.96/1.28
% 3.96/1.28
%------------------------------------------------------------------------------