%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 2.62s 1.28s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% 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 : 32 ( 0 sgn 32 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
fof(f13,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
fof(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
fof(f17,negated_conjecture,
add(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_a_is_a) ).
fof(f18,plain,
a != add(a,a),
inference(reorient_equations,[],[f17]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
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_76,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f15]) ).
tcf(c_77,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_78,negated_conjecture,
add(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_284,plain,
! [X0: $i] : add(multiply(additive_identity,X0),multiplicative_identity) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_239,c_75]) ).
tcf(c_332,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_284,c_64]) ).
tcf(c_336,plain,
add(multiplicative_identity,multiplicative_identity) = add(multiplicative_identity,additive_identity),
inference(superposition,[status(thm)],[c_74,c_332]) ).
tcf(c_356,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_336,c_76]) ).
tcf(c_579,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_2027,plain,
! [X0: $i] : add(X0,multiply(multiplicative_identity,X0)) = multiply(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_356,c_579]) ).
tcf(c_2060,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2027,c_75]) ).
tcf(c_2066,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_78,c_2060]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 06:24:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running UEQ theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.62/1.28 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.62/1.28 % SZS status Started for theBenchmark.p
% 2.62/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.62/1.28
% 2.62/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.62/1.28
% 2.62/1.28 % ------ iProver source info
% 2.62/1.28
% 2.62/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.62/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.62/1.28 % git: non_committed_changes: false
% 2.62/1.28
% 2.62/1.28 % ------ Parsing...% successful
% 2.62/1.28
% 2.62/1.28
% 2.62/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.62/1.28
% 2.62/1.28 % ------ 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 %
% 2.62/1.28
% 2.62/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.62/1.28
% 2.62/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.62/1.28 % ------ Proving...
% 2.62/1.28 % ------ Problem Properties
% 2.62/1.28
% 2.62/1.28 %
% 2.62/1.28 % clauses 13
% 2.62/1.28 % conjectures 1
% 2.62/1.28 % EPR 0
% 2.62/1.28 % Horn 13
% 2.62/1.28 % unary 13
% 2.62/1.28 % binary 0
% 2.62/1.28 % lits 13
% 2.62/1.28 % lits eq 13
% 2.62/1.28 % fd_pure 0
% 2.62/1.28 % fd_pseudo 0
% 2.62/1.28 % fd_cond 0
% 2.62/1.28 % fd_pseudo_cond 0
% 2.62/1.28 % AC symbols 0
% 2.62/1.28
% 2.62/1.28 % ------ Input Options Time Limit: Unbounded
% 2.62/1.28
% 2.62/1.28
% 2.62/1.28 % ------
% 2.62/1.28 % Current options:
% 2.62/1.28 % ------
% 2.62/1.28
% 2.62/1.28
% 2.62/1.28 %
% 2.62/1.28
% 2.62/1.28 % ------ Proving...
% 2.62/1.28 %
% 2.62/1.28
% 2.62/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.62/1.28
% 2.62/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.62/1.28
% 2.62/1.28
%------------------------------------------------------------------------------