%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO005-2 : 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 : n003.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 2.59s 1.20s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 89 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
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(f4,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
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(f6,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
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(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
fof(f17,negated_conjecture,
add(a,multiplicative_identity) != multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_plus_1_is_a) ).
fof(f18,plain,
multiplicative_identity != add(a,multiplicative_identity),
inference(reorient_equations,[],[f17]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
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_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
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_69,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f7]) ).
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,multiplicative_identity) != multiplicative_identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_123,plain,
add(multiplicative_identity,a) != multiplicative_identity,
inference(demodulation,[status(thm)],[c_78,c_64]) ).
tcf(c_240,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_245,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = add(multiply(X0,additive_identity),X1),
inference(superposition,[status(thm)],[c_77,c_66]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_70,c_67]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_76,c_67]) ).
tcf(c_285,plain,
! [X0: $i] : add(multiply(additive_identity,X0),multiplicative_identity) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_240,c_75]) ).
tcf(c_321,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_285,c_64]) ).
tcf(c_325,plain,
add(multiplicative_identity,multiplicative_identity) = add(multiplicative_identity,additive_identity),
inference(superposition,[status(thm)],[c_74,c_321]) ).
tcf(c_360,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_325,c_76]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),X1) = add(multiply(additive_identity,X0),X1),
inference(demodulation,[status(thm)],[c_245,c_65,c_240]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] : add(multiply(additive_identity,X0),X1) = add(X1,multiply(X0,additive_identity)),
inference(superposition,[status(thm)],[c_435,c_64]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),X1) = add(X1,multiply(additive_identity,X0)),
inference(superposition,[status(thm)],[c_435,c_64]) ).
tcf(c_605,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_735,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,multiplicative_identity)),
inference(superposition,[status(thm)],[c_74,c_69]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_64,c_260]) ).
tcf(c_986,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_260,c_75]) ).
tcf(c_1070,plain,
! [X0: $i] : add(multiplicative_identity,multiply(X0,additive_identity)) = add(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_65,c_986]) ).
tcf(c_1974,plain,
! [X0: $i] : add(X0,multiply(multiplicative_identity,X0)) = multiply(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_360,c_605]) ).
tcf(c_2013,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_1974,c_75]) ).
tcf(c_2117,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c_2013,c_66]) ).
tcf(c_2133,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X0) = add(X0,multiply(additive_identity,X1)),
inference(light_normalisation,[status(thm)],[c_2117,c_965]) ).
tcf(c_2861,plain,
! [X0: $i,X1: $i] : add(X0,multiply(additive_identity,X1)) = multiply(X0,add(X1,multiplicative_identity)),
inference(light_normalisation,[status(thm)],[c_735,c_2133]) ).
tcf(c_4286,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_259,c_75]) ).
tcf(c_4299,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_74,c_4286]) ).
tcf(c_4335,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(light_normalisation,[status(thm)],[c_4299,c_70]) ).
tcf(c_4351,plain,
! [X0: $i,X1: $i] : add(X0,multiply(additive_identity,X1)) = multiply(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_2861,c_4335]) ).
tcf(c_4352,plain,
! [X0: $i,X1: $i] : add(X0,multiply(additive_identity,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_4351,c_74]) ).
tcf(c_4356,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),X1) = X1,
inference(demodulation,[status(thm)],[c_458,c_4352]) ).
tcf(c_4357,plain,
! [X0: $i,X1: $i] : add(multiply(additive_identity,X0),X1) = X1,
inference(demodulation,[status(thm)],[c_435,c_4356]) ).
tcf(c_4359,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,additive_identity)) = X0,
inference(demodulation,[status(thm)],[c_449,c_4357]) ).
tcf(c_4363,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_1070,c_4359]) ).
tcf(c_4364,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_123,c_4363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n003.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 06:28:08 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running UEQ theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.59/1.20 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.59/1.20 % SZS status Started for theBenchmark.p
% 2.59/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.59/1.20
% 2.59/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.59/1.20
% 2.59/1.20 % ------ iProver source info
% 2.59/1.20
% 2.59/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.59/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.59/1.20 % git: non_committed_changes: false
% 2.59/1.20
% 2.59/1.20 % ------ Parsing...% successful
% 2.59/1.20
% 2.59/1.20
% 2.59/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.59/1.20
% 2.59/1.20 % ------ Preprocessing... sup_sim: 5 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 %
% 2.59/1.20
% 2.59/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.59/1.20
% 2.59/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.59/1.20 % ------ Proving...
% 2.59/1.20 % ------ Problem Properties
% 2.59/1.20
% 2.59/1.20 %
% 2.59/1.20 % clauses 13
% 2.59/1.20 % conjectures 0
% 2.59/1.20 % EPR 0
% 2.59/1.20 % Horn 13
% 2.59/1.20 % unary 13
% 2.59/1.20 % binary 0
% 2.59/1.20 % lits 13
% 2.59/1.20 % lits eq 13
% 2.59/1.20 % fd_pure 0
% 2.59/1.20 % fd_pseudo 0
% 2.59/1.20 % fd_cond 0
% 2.59/1.20 % fd_pseudo_cond 0
% 2.59/1.20 % AC symbols 0
% 2.59/1.20
% 2.59/1.20 % ------ Input Options Time Limit: Unbounded
% 2.59/1.20
% 2.59/1.20
% 2.59/1.20 % ------
% 2.59/1.20 % Current options:
% 2.59/1.20 % ------
% 2.59/1.20
% 2.59/1.20
% 2.59/1.20 %
% 2.59/1.20
% 2.59/1.20 % ------ Proving...
% 2.59/1.20 %
% 2.59/1.20
% 2.59/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.59/1.20
% 2.59/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.59/1.20
% 2.59/1.20
%------------------------------------------------------------------------------