%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 01:00:08 PM UTC 2026
% Result : Unsatisfiable 3.11s 1.27s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 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 : 3 ( 1 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
fof(f13,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
fof(f17,negated_conjecture,
multiply(a,a) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_a_is_a) ).
fof(f18,plain,
a != multiply(a,a),
inference(reorient_equations,[],[f17]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
tcf(c_77,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_78,negated_conjecture,
multiply(a,a) != a,
inference(cnf_transformation,[],[f18]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_77,c_66]) ).
tcf(c_278,plain,
! [X0: $i] : add(multiply(additive_identity,additive_identity),X0) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_77,c_239]) ).
tcf(c_286,plain,
! [X0: $i] : multiply(X0,add(multiplicative_identity,X0)) = add(additive_identity,X0),
inference(superposition,[status(thm)],[c_74,c_239]) ).
tcf(c_297,plain,
! [X0: $i] : multiply(X0,add(multiplicative_identity,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_286,c_77]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_75,c_68]) ).
tcf(c_2248,plain,
! [X0: $i] : multiply(add(multiplicative_identity,X0),additive_identity) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_618,c_77]) ).
tcf(c_2358,plain,
! [X0: $i] : multiply(additive_identity,add(multiplicative_identity,X0)) = multiply(X0,additive_identity),
inference(demodulation,[status(thm)],[c_2248,c_65]) ).
tcf(c_2383,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_2358,c_297]) ).
tcf(c_2391,plain,
! [X0: $i] : multiply(X0,X0) = add(additive_identity,X0),
inference(demodulation,[status(thm)],[c_278,c_2383]) ).
tcf(c_2392,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2391,c_77]) ).
tcf(c_2393,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_78,c_2392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.34 % Computer : n004.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Fri Sep 25 06:27:06 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running UEQ theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 3.11/1.27 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.11/1.27 % SZS status Started for theBenchmark.p
% 3.11/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.11/1.27
% 3.11/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.11/1.27
% 3.11/1.27 % ------ iProver source info
% 3.11/1.27
% 3.11/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.11/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.11/1.27 % git: non_committed_changes: false
% 3.11/1.27
% 3.11/1.27 % ------ Parsing...% successful
% 3.11/1.27
% 3.11/1.27
% 3.11/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.11/1.27
% 3.11/1.27 % ------ Preprocessing... sup_sim: 4 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.11/1.27
% 3.11/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.11/1.27
% 3.11/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.11/1.27 % ------ Proving...
% 3.11/1.27 % ------ Problem Properties
% 3.11/1.27
% 3.11/1.27 %
% 3.11/1.27 % clauses 13
% 3.11/1.27 % conjectures 1
% 3.11/1.27 % EPR 0
% 3.11/1.27 % Horn 13
% 3.11/1.27 % unary 13
% 3.11/1.27 % binary 0
% 3.11/1.27 % lits 13
% 3.11/1.27 % lits eq 13
% 3.11/1.27 % fd_pure 0
% 3.11/1.27 % fd_pseudo 0
% 3.11/1.27 % fd_cond 0
% 3.11/1.27 % fd_pseudo_cond 0
% 3.11/1.27 % AC symbols 0
% 3.11/1.27
% 3.11/1.27 % ------ Input Options Time Limit: Unbounded
% 3.11/1.27
% 3.11/1.27
% 3.11/1.27 % ------
% 3.11/1.27 % Current options:
% 3.11/1.27 % ------
% 3.11/1.27
% 3.11/1.27
% 3.11/1.27 %
% 3.11/1.27
% 3.11/1.27 % ------ Proving...
% 3.11/1.27 %
% 3.11/1.27
% 3.11/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.11/1.27
% 3.11/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.11/1.27
% 3.11/1.27
%------------------------------------------------------------------------------