%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:15:47 PM UTC 2026
% Result : Unsatisfiable 10.49s 2.46s
% Output : CNFRefutation 10.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 21 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 64 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
fof(f30,axiom,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
fof(f33,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
fof(f34,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_8) ).
fof(f35,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_9) ).
fof(f36,negated_conjecture,
product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_10) ).
fof(f37,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_11) ).
fof(f38,negated_conjecture,
~ product(b,c,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_12) ).
tcf(c_88,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_89,plain,
defined(c),
inference(cnf_transformation,[],[f29]) ).
tcf(c_90,plain,
defined(d),
inference(cnf_transformation,[],[f30]) ).
tcf(c_93,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f33]) ).
tcf(c_94,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(cnf_transformation,[],[f34]) ).
tcf(c_95,negated_conjecture,
product(a,multiplicative_inverse(b),s),
inference(cnf_transformation,[],[f35]) ).
tcf(c_96,negated_conjecture,
product(c,multiplicative_inverse(d),s),
inference(cnf_transformation,[],[f36]) ).
tcf(c_97,negated_conjecture,
product(a,d,k),
inference(cnf_transformation,[],[f37]) ).
tcf(c_98,negated_conjecture,
~ product(b,c,k),
inference(cnf_transformation,[],[f38]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_110,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_113,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_228,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_229,plain,
( sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity)
| ~ defined(d) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_233,plain,
( product(multiplicative_inverse(b),a,s)
| ~ product(a,multiplicative_inverse(b),s) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_236,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(s,X0,X2)
| ~ product(c,X1,X2)
| ~ product(c,multiplicative_inverse(d),s)
| ~ product(multiplicative_inverse(d),X0,X1) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_272,plain,
( product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_inverse(b),X1,X2)
| ~ product(s,X0,X2)
| ~ product(a,X0,X1)
| ~ product(multiplicative_inverse(b),a,s) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_389,plain,
( product(c,multiplicative_identity,c)
| ~ product(multiplicative_identity,c,c) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_390,plain,
! [X0: $i] :
( product(s,X0,c)
| ~ product(c,multiplicative_identity,c)
| ~ product(c,multiplicative_inverse(d),s)
| ~ product(multiplicative_inverse(d),X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_248]) ).
tcf(c_477,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_113,c_106]) ).
tcf(c_666,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(b,X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(multiplicative_inverse(b),X0,X1) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_748,plain,
( product(multiplicative_identity,c,c)
| ~ defined(c) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,k)
| ~ product(a,X0,X2)
| ~ product(X0,X1,d) ),
inference(superposition,[status(thm)],[c_97,c_107]) ).
tcf(c_1050,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,k)
| ~ defined(d)
| ~ product(a,d,X0) ),
inference(superposition,[status(thm)],[c_477,c_790]) ).
tcf(c_1051,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,k)
| ~ product(a,d,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1050,c_90]) ).
tcf(c_1343,plain,
( product(s,d,c)
| ~ product(c,multiplicative_identity,c)
| ~ product(c,multiplicative_inverse(d),s)
| ~ product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_390]) ).
tcf(c_1409,plain,
! [X0: $i] :
( product(multiplicative_inverse(b),k,X0)
| ~ product(a,d,k)
| ~ product(s,d,X0)
| ~ product(multiplicative_inverse(b),a,s) ),
inference(instantiation,[status(thm)],[c_294]) ).
tcf(c_1615,plain,
product(k,multiplicative_identity,k),
inference(superposition,[status(thm)],[c_97,c_1051]) ).
tcf(c_2165,plain,
product(multiplicative_identity,k,k),
inference(superposition,[status(thm)],[c_1615,c_106]) ).
tcf(c_3313,plain,
( product(multiplicative_inverse(b),k,c)
| ~ product(s,d,c)
| ~ product(a,d,k)
| ~ product(multiplicative_inverse(b),a,s) ),
inference(instantiation,[status(thm)],[c_1409]) ).
tcf(c_12427,plain,
! [X0: $i] :
( product(b,c,X0)
| ~ product(multiplicative_identity,k,X0)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(multiplicative_inverse(b),k,c) ),
inference(instantiation,[status(thm)],[c_666]) ).
tcf(c_30828,plain,
( product(b,c,k)
| ~ product(multiplicative_identity,k,k)
| ~ product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ product(multiplicative_inverse(b),k,c) ),
inference(instantiation,[status(thm)],[c_12427]) ).
tcf(c_30829,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_30828,c_3313,c_2165,c_1343,c_748,c_389,c_272,c_233,c_229,c_228,c_93,c_94,c_95,c_96,c_98,c_97,c_88,c_89,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n009.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 10:53:29 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.64
% 0.13/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.64
% 0.13/0.64 % Detected problem language: tptp
% 0.13/0.65 % Proving...
% 10.49/2.46 % SZS status Started for theBenchmark.p
% 10.49/2.46 % SZS status Unsatisfiable for theBenchmark.p
% 10.49/2.46
% 10.49/2.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.49/2.46
% 10.49/2.46 % ------ iProver source info
% 10.49/2.46
% 10.49/2.46 % git: date: 2026-07-19 20:42:38 +0200
% 10.49/2.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.49/2.46 % git: non_committed_changes: false
% 10.49/2.46
% 10.49/2.46 % ------ Parsing...% successful
% 10.49/2.46
% 10.49/2.46
% 10.49/2.46 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.49/2.46
% 10.49/2.46 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.49/2.46
% 10.49/2.46 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.49/2.46 % ------ Proving...
% 10.49/2.46 % ------ Problem Properties
% 10.49/2.46
% 10.49/2.46 %
% 10.49/2.46 % clauses 27
% 10.49/2.46 % conjectures 6
% 10.49/2.46 % EPR 23
% 10.49/2.46 % Horn 25
% 10.49/2.46 % unary 15
% 10.49/2.46 % binary 4
% 10.49/2.46 % lits 55
% 10.49/2.46 % lits eq 0
% 10.49/2.46 % fd_pure 0
% 10.49/2.46 % fd_pseudo 0
% 10.49/2.46 % fd_cond 0
% 10.49/2.46 % fd_pseudo_cond 0
% 10.49/2.46 % AC symbols 0
% 10.49/2.46
% 10.49/2.46 % ------ Schedule dynamic 5 is on
% 10.49/2.46
% 10.49/2.46 % ------ no equalities: superposition off
% 10.49/2.46
% 10.49/2.46 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.49/2.46
% 10.49/2.46
% 10.49/2.46 % ------
% 10.49/2.46 % Current options:
% 10.49/2.46 % ------
% 10.49/2.46
% 10.49/2.46
% 10.49/2.46 %
% 10.49/2.46
% 10.49/2.46 % ------ Proving...
% 10.49/2.46 %
% 10.49/2.46
% 10.49/2.46 % SZS status Unsatisfiable for theBenchmark.p
% 10.49/2.46
% 10.49/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.49/2.46
% 10.49/2.46
%------------------------------------------------------------------------------