%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP166-2 : 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 01:31:37 PM UTC 2026
% Result : Unsatisfiable 2.20s 6.18s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 28 :)
% 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(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
fof(f19,axiom,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat2b_2) ).
fof(f20,plain,
identity = greatest_lower_bound(b,identity),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
greatest_lower_bound(a,multiply(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat2b) ).
fof(f22,plain,
a != greatest_lower_bound(a,multiply(a,b)),
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_79,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_83,plain,
greatest_lower_bound(b,identity) = identity,
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
greatest_lower_bound(a,multiply(a,b)) != a,
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,plain,
greatest_lower_bound(identity,b) = identity,
inference(theory_normalisation,[status(thm)],[c_83,c_73,c_71,c_72,c_70]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_2029,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_252,c_67]) ).
tcf(c_2031,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_68,c_2029]) ).
tcf(c_2033,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_2029,c_2029]) ).
tcf(c_2122,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_2031,c_2033]) ).
tcf(c_2129,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
inference(superposition,[status(thm)],[c_2122,c_79]) ).
tcf(c_2144,plain,
multiply(a,greatest_lower_bound(identity,b)) != a,
inference(demodulation,[status(thm)],[c_84,c_2129]) ).
tcf(c_2145,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2144,c_101,c_2122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n008.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 13:56:18 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running UEQ theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 2.20/6.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.20/6.18 % SZS status Started for theBenchmark.p
% 2.20/6.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.20/6.18
% 2.20/6.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.20/6.18
% 2.20/6.18 % ------ iProver source info
% 2.20/6.18
% 2.20/6.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.20/6.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.20/6.18 % git: non_committed_changes: false
% 2.20/6.18
% 2.20/6.18 % ------ Parsing...% successful
% 2.20/6.18
% 2.20/6.18
% 2.20/6.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.20/6.18
% 2.20/6.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.20/6.18
% 2.20/6.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.20/6.18
% 2.20/6.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.20/6.18 % ------ Proving...
% 2.20/6.18 % ------ Problem Properties
% 2.20/6.18
% 2.20/6.18 %
% 2.20/6.18 % clauses 18
% 2.20/6.18 % conjectures 1
% 2.20/6.18 % EPR 0
% 2.20/6.18 % Horn 18
% 2.20/6.18 % unary 18
% 2.20/6.18 % binary 0
% 2.20/6.18 % lits 18
% 2.20/6.18 % lits eq 18
% 2.20/6.18 % fd_pure 0
% 2.20/6.18 % fd_pseudo 0
% 2.20/6.18 % fd_cond 0
% 2.20/6.18 % fd_pseudo_cond 0
% 2.20/6.18 % AC symbols 2
% 2.20/6.18
% 2.20/6.18 % ------ Input Options Time Limit: Unbounded
% 2.20/6.18
% 2.20/6.18
% 2.20/6.18 % ------
% 2.20/6.18 % Current options:
% 2.20/6.18 % ------
% 2.20/6.18
% 2.20/6.18
% 2.20/6.18 %
% 2.20/6.18
% 2.20/6.18 % ------ Proving...
% 2.20/6.18 %
% 2.20/6.18
% 2.20/6.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.20/6.18
% 2.20/6.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.20/6.18
% 2.20/6.18
%------------------------------------------------------------------------------