%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO006-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 2.19s 1.27s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 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 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
multiply(a,additive_identity) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_identity) ).
fof(f12,plain,
additive_identity != multiply(a,additive_identity),
inference(reorient_equations,[],[f11]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
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_64,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,negated_conjecture,
multiply(a,additive_identity) != additive_identity,
inference(cnf_transformation,[],[f12]) ).
tcf(c_93,plain,
multiply(additive_identity,a) != additive_identity,
inference(demodulation,[status(thm)],[c_66,c_59]) ).
tcf(c_141,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(superposition,[status(thm)],[c_62,c_58]) ).
tcf(c_153,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[status(thm)],[c_63,c_59]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_64,c_60]) ).
tcf(c_182,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_187,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,multiplicative_identity)),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_509,plain,
! [X0: $i] : multiply(additive_identity,add(multiplicative_identity,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_182,c_141]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,multiplicative_identity)) = multiply(X0,add(multiplicative_identity,X1)),
inference(demodulation,[status(thm)],[c_187,c_58,c_182]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_163,c_153]) ).
tcf(c_810,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_63,c_806]) ).
tcf(c_828,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(light_normalisation,[status(thm)],[c_810,c_64]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i] : multiply(X0,add(multiplicative_identity,X1)) = multiply(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_567,c_828]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] : multiply(X0,add(multiplicative_identity,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_838,c_63]) ).
tcf(c_840,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_509,c_839]) ).
tcf(c_842,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO006-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 06:30:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running UEQ theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.19/1.27 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.19/1.27 % SZS status Started for theBenchmark.p
% 2.19/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.19/1.27
% 2.19/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.19/1.27
% 2.19/1.27 % ------ iProver source info
% 2.19/1.27
% 2.19/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.19/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.19/1.27 % git: non_committed_changes: false
% 2.19/1.27
% 2.19/1.27 % ------ Parsing...% successful
% 2.19/1.27
% 2.19/1.27
% 2.19/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.19/1.27
% 2.19/1.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.19/1.27
% 2.19/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.19/1.27
% 2.19/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.19/1.27 % ------ Proving...
% 2.19/1.27 % ------ Problem Properties
% 2.19/1.27
% 2.19/1.27 %
% 2.19/1.27 % clauses 9
% 2.19/1.27 % conjectures 0
% 2.19/1.27 % EPR 0
% 2.19/1.27 % Horn 9
% 2.19/1.27 % unary 9
% 2.19/1.27 % binary 0
% 2.19/1.27 % lits 9
% 2.19/1.27 % lits eq 9
% 2.19/1.27 % fd_pure 0
% 2.19/1.27 % fd_pseudo 0
% 2.19/1.27 % fd_cond 0
% 2.19/1.27 % fd_pseudo_cond 0
% 2.19/1.27 % AC symbols 0
% 2.19/1.27
% 2.19/1.27 % ------ Input Options Time Limit: Unbounded
% 2.19/1.27
% 2.19/1.27
% 2.19/1.27 % ------
% 2.19/1.27 % Current options:
% 2.19/1.27 % ------
% 2.19/1.27
% 2.19/1.27
% 2.19/1.27 %
% 2.19/1.27
% 2.19/1.27 % ------ Proving...
% 2.19/1.27 %
% 2.19/1.27
% 2.19/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.19/1.27
% 2.19/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/1.27
% 2.19/1.27
%------------------------------------------------------------------------------