%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO012-2 : 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 : 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 01:00:12 PM UTC 2026
% Result : Unsatisfiable 2.73s 1.28s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 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 : 53 ( 0 sgn 53 !; 0 ?; 36 :)
% 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(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(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
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(f17,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f18,plain,
x != inverse(inverse(x)),
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_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_72,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
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_78,negated_conjecture,
inverse(inverse(x)) != x,
inference(cnf_transformation,[],[f18]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_70,c_66]) ).
tcf(c_266,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_533,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X0,X1)) = add(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c_245,c_64,c_75]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X1,X0)) = add(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_65,c_533]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] : add(X0,multiply(multiplicative_identity,X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_75,c_69]) ).
tcf(c_1452,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,multiply(multiplicative_identity,X1)),
inference(light_normalisation,[status(thm)],[c_266,c_673]) ).
tcf(c_1453,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_1452,c_75]) ).
tcf(c_1463,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_72,c_1453]) ).
tcf(c_1491,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_1463,c_76]) ).
tcf(c_2226,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = add(inverse(inverse(X0)),additive_identity),
inference(superposition,[status(thm)],[c_72,c_537]) ).
tcf(c_2245,plain,
! [X0: $i] : add(inverse(inverse(X0)),additive_identity) = X0,
inference(light_normalisation,[status(thm)],[c_2226,c_1491]) ).
tcf(c_2287,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_2245,c_76]) ).
tcf(c_2288,plain,
x != x,
inference(demodulation,[status(thm)],[c_78,c_2287]) ).
tcf(c_2290,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 06:29:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running UEQ theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.73/1.28 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.73/1.28 % SZS status Started for theBenchmark.p
% 2.73/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/1.28
% 2.73/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/1.28
% 2.73/1.28 % ------ iProver source info
% 2.73/1.28
% 2.73/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/1.28 % git: non_committed_changes: false
% 2.73/1.28
% 2.73/1.28 % ------ Parsing...% successful
% 2.73/1.28
% 2.73/1.28
% 2.73/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.73/1.28
% 2.73/1.28 % ------ 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 %
% 2.73/1.28
% 2.73/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.73/1.28
% 2.73/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.73/1.28 % ------ Proving...
% 2.73/1.28 % ------ Problem Properties
% 2.73/1.28
% 2.73/1.28 %
% 2.73/1.28 % clauses 13
% 2.73/1.28 % conjectures 1
% 2.73/1.28 % EPR 0
% 2.73/1.28 % Horn 13
% 2.73/1.28 % unary 13
% 2.73/1.28 % binary 0
% 2.73/1.28 % lits 13
% 2.73/1.28 % lits eq 13
% 2.73/1.28 % fd_pure 0
% 2.73/1.28 % fd_pseudo 0
% 2.73/1.28 % fd_cond 0
% 2.73/1.28 % fd_pseudo_cond 0
% 2.73/1.28 % AC symbols 0
% 2.73/1.28
% 2.73/1.28 % ------ Input Options Time Limit: Unbounded
% 2.73/1.28
% 2.73/1.28
% 2.73/1.28 % ------
% 2.73/1.28 % Current options:
% 2.73/1.28 % ------
% 2.73/1.28
% 2.73/1.28
% 2.73/1.28 %
% 2.73/1.28
% 2.73/1.28 % ------ Proving...
% 2.73/1.28 %
% 2.73/1.28
% 2.73/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/1.28
% 2.73/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/1.28
% 2.73/1.28
%------------------------------------------------------------------------------