%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% 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 01:00:09 PM UTC 2026
% Result : Unsatisfiable 0.37s 1.15s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 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 : 28 ( 0 sgn 28 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
fof(f11,negated_conjecture,
add(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_a_is_a) ).
fof(f12,plain,
a != add(a,a),
inference(reorient_equations,[],[f11]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_63,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_66,negated_conjecture,
add(a,a) != a,
inference(cnf_transformation,[],[f12]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_62,c_60]) ).
tcf(c_176,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[status(thm)],[c_59,c_63]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_230,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_155,c_176]) ).
tcf(c_291,plain,
add(multiplicative_identity,additive_identity) = add(multiplicative_identity,multiplicative_identity),
inference(superposition,[status(thm)],[c_63,c_230]) ).
tcf(c_329,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_291,c_62]) ).
tcf(c_601,plain,
! [X0: $i] : add(X0,multiply(X0,multiplicative_identity)) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_329,c_183]) ).
tcf(c_617,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_601,c_63]) ).
tcf(c_625,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n008.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 : Fri Sep 25 06:27:25 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 Running UEQ theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 0.37/1.15 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 0.37/1.15 % SZS status Started for theBenchmark.p
% 0.37/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 0.37/1.15
% 0.37/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.37/1.15
% 0.37/1.15 % ------ iProver source info
% 0.37/1.15
% 0.37/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 0.37/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.37/1.15 % git: non_committed_changes: false
% 0.37/1.15
% 0.37/1.15 % ------ Parsing...% successful
% 0.37/1.15
% 0.37/1.15
% 0.37/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.37/1.15
% 0.37/1.15 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.37/1.15
% 0.37/1.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.37/1.15
% 0.37/1.15 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.37/1.15 % ------ Proving...
% 0.37/1.15 % ------ Problem Properties
% 0.37/1.15
% 0.37/1.15 %
% 0.37/1.15 % clauses 9
% 0.37/1.15 % conjectures 1
% 0.37/1.15 % EPR 0
% 0.37/1.15 % Horn 9
% 0.37/1.15 % unary 9
% 0.37/1.15 % binary 0
% 0.37/1.15 % lits 9
% 0.37/1.15 % lits eq 9
% 0.37/1.15 % fd_pure 0
% 0.37/1.15 % fd_pseudo 0
% 0.37/1.15 % fd_cond 0
% 0.37/1.15 % fd_pseudo_cond 0
% 0.37/1.15 % AC symbols 0
% 0.37/1.15
% 0.37/1.15 % ------ Input Options Time Limit: Unbounded
% 0.37/1.15
% 0.37/1.15
% 0.37/1.15 % ------
% 0.37/1.15 % Current options:
% 0.37/1.15 % ------
% 0.37/1.15
% 0.37/1.15
% 0.37/1.15 %
% 0.37/1.15
% 0.37/1.15 % ------ Proving...
% 0.37/1.15 %
% 0.37/1.15
% 0.37/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 0.37/1.15
% 0.37/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.37/1.15
% 0.37/1.15
%------------------------------------------------------------------------------