%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD009-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 01:15:35 PM UTC 2026
% Result : Unsatisfiable 2.26s 1.75s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 53 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( ~ defined(X2)
| ~ defined(X1)
| ~ defined(X0)
| equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
fof(f6,axiom,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
fof(f7,axiom,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
fof(f15,axiom,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
fof(f25,axiom,
! [X2,X0,X1] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
fof(f31,negated_conjecture,
! [X0] : ~ equalish(multiply(a,X0),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_not_equal_to_b_4) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2))
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_85,plain,
! [X0: $i] :
( equalish(multiply(multiplicative_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_86,plain,
! [X0: $i] :
( equalish(X0,additive_identity)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_94,plain,
! [X0: $i] :
( equalish(X0,additive_identity)
| defined(multiplicative_inverse(X0))
| ~ defined(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ defined(X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_107,plain,
defined(a),
inference(cnf_transformation,[],[f28]) ).
tcf(c_108,plain,
defined(b),
inference(cnf_transformation,[],[f29]) ).
tcf(c_109,negated_conjecture,
~ equalish(a,additive_identity),
inference(cnf_transformation,[],[f30]) ).
tcf(c_110,negated_conjecture,
! [X0: $i] : ~ equalish(multiply(a,X0),b),
inference(cnf_transformation,[],[f31]) ).
tcf(c_284,negated_conjecture,
! [X0: $i] : ~ equalish(multiply(a,X0),b),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_286,plain,
( equalish(a,additive_identity)
| defined(multiplicative_inverse(a))
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_287,plain,
( equalish(a,additive_identity)
| equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] :
( equalish(multiply(a,X0),b)
| ~ equalish(X1,b)
| ~ equalish(multiply(a,X0),X1) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_327,plain,
( equalish(multiply(multiplicative_identity,b),b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( equalish(X0,b)
| ~ equalish(X1,b)
| ~ equalish(X0,X1) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_447,plain,
! [X0: $i] :
( equalish(X0,b)
| ~ equalish(multiply(multiplicative_identity,b),b)
| ~ equalish(X0,multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_334]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( equalish(multiply(a,multiply(X0,X1)),b)
| ~ equalish(multiply(multiply(a,X0),X1),b)
| ~ equalish(multiply(a,multiply(X0,X1)),multiply(multiply(a,X0),X1)) ),
inference(instantiation,[status(thm)],[c_297]) ).
tcf(c_615,plain,
! [X0: $i,X1: $i] :
( equalish(multiply(a,multiply(X0,X1)),multiply(multiply(a,X0),X1))
| ~ defined(a)
| ~ defined(X1)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_1099,plain,
! [X0: $i] :
( equalish(multiply(X0,b),multiply(multiplicative_identity,b))
| ~ defined(b)
| ~ equalish(X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_3520,plain,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b))
| ~ defined(b)
| ~ equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_1099]) ).
tcf(c_3750,plain,
! [X0: $i,X1: $i] :
( equalish(multiply(multiply(a,X0),X1),b)
| ~ equalish(multiply(multiplicative_identity,b),b)
| ~ equalish(multiply(multiply(a,X0),X1),multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_6527,plain,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),b),b)
| ~ equalish(multiply(multiplicative_identity,b),b)
| ~ equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_3750]) ).
tcf(c_13260,plain,
( equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b)
| ~ equalish(multiply(multiply(a,multiplicative_inverse(a)),b),b)
| ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiply(a,multiplicative_inverse(a)),b)) ),
inference(instantiation,[status(thm)],[c_614]) ).
tcf(c_13270,plain,
( equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiply(a,multiplicative_inverse(a)),b))
| ~ defined(b)
| ~ defined(a)
| ~ defined(multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_615]) ).
tcf(c_24053,plain,
~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b),
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_24054,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24053,c_13270,c_13260,c_6527,c_3520,c_327,c_287,c_286,c_109,c_107,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD009-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n002.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 10:38:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.26/1.75 % SZS status Started for theBenchmark.p
% 2.26/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.26/1.75
% 2.26/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.26/1.75
% 2.26/1.75 % ------ iProver source info
% 2.26/1.75
% 2.26/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 2.26/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.26/1.75 % git: non_committed_changes: false
% 2.26/1.75
% 2.26/1.75 % ------ Parsing...% successful
% 2.26/1.75
% 2.26/1.75
% 2.26/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.26/1.75
% 2.26/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.26/1.75
% 2.26/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.26/1.75 % ------ Proving...
% 2.26/1.75 % ------ Problem Properties
% 2.26/1.75
% 2.26/1.75 %
% 2.26/1.75 % clauses 31
% 2.26/1.75 % conjectures 2
% 2.26/1.75 % EPR 13
% 2.26/1.75 % Horn 28
% 2.26/1.75 % unary 7
% 2.26/1.75 % binary 6
% 2.26/1.75 % lits 77
% 2.26/1.75 % lits eq 0
% 2.26/1.75 % fd_pure 0
% 2.26/1.75 % fd_pseudo 0
% 2.26/1.75 % fd_cond 0
% 2.26/1.75 % fd_pseudo_cond 0
% 2.26/1.75 % AC symbols 0
% 2.26/1.75
% 2.26/1.75 % ------ Schedule dynamic 5 is on
% 2.26/1.75
% 2.26/1.75 % ------ no equalities: superposition off
% 2.26/1.75
% 2.26/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.26/1.75
% 2.26/1.75
% 2.26/1.75 % ------
% 2.26/1.75 % Current options:
% 2.26/1.75 % ------
% 2.26/1.75
% 2.26/1.75
% 2.26/1.75 %
% 2.26/1.75
% 2.26/1.75 % ------ Proving...
% 2.26/1.75 %
% 2.26/1.75
% 2.26/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.26/1.75
% 2.26/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.26/1.75
% 2.26/1.75
%------------------------------------------------------------------------------