%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD029-3 : 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 : 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 01:15:41 PM UTC 2026
% Result : Unsatisfiable 10.26s 2.75s
% Output : CNFRefutation 10.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 24 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 204 ( 102 ~; 102 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 66 :)
% 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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f20,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
fof(f30,axiom,
defined(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
fof(f32,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
fof(f33,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
fof(f34,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
tcf(c_88,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_89,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_90,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_91,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_99,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_100,plain,
! [X0: $i] :
( defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_110,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_111,plain,
defined(u),
inference(cnf_transformation,[],[f29]) ).
tcf(c_112,plain,
defined(v),
inference(cnf_transformation,[],[f30]) ).
tcf(c_113,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f31]) ).
tcf(c_114,negated_conjecture,
product(a,u,b),
inference(cnf_transformation,[],[f32]) ).
tcf(c_115,negated_conjecture,
product(a,v,b),
inference(cnf_transformation,[],[f33]) ).
tcf(c_116,negated_conjecture,
~ product(multiplicative_identity,u,v),
inference(cnf_transformation,[],[f34]) ).
tcf(c_299,negated_conjecture,
product(a,u,b),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_300,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_302,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_305,plain,
( product(u,a,b)
| ~ product(a,u,b) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(multiplicative_identity,X2,X3)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X1,X3)
| ~ product(multiplicative_identity,X2,X3)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X2,X1)
| ~ product(b,X2,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_inverse(b),X0,X1) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_inverse(b),X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(b,X0,X1)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(b,X0,X2)
| ~ product(u,a,b)
| ~ product(u,X1,X2)
| ~ product(a,X0,X1) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(u,X1,X2)
| ~ product(u,a,b)
| ~ product(b,X0,X2)
| ~ product(a,X0,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_393,plain,
! [X0: $i] :
( product(b,X0,multiply(b,X0))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X0,X2)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X1,X2)
| ~ product(multiplicative_identity,X0,X1) ),
inference(instantiation,[status(thm)],[c_327]) ).
tcf(c_994,plain,
( product(multiplicative_identity,v,v)
| ~ defined(v) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X2,v)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(X0,X1,v)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_321]) ).
tcf(c_1868,plain,
! [X0: $i] :
( product(b,u,X0)
| ~ product(u,a,b)
| ~ product(a,u,b)
| ~ product(u,b,X0) ),
inference(instantiation,[status(thm)],[c_350]) ).
tcf(c_1884,plain,
! [X0: $i] :
( product(u,b,X0)
| ~ product(u,a,b)
| ~ product(a,v,b)
| ~ product(b,v,X0) ),
inference(instantiation,[status(thm)],[c_351]) ).
tcf(c_3247,plain,
! [X0: $i] :
( product(multiplicative_identity,u,v)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,u,X0)
| ~ product(multiplicative_identity,X0,v) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_4048,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_4801,plain,
( product(u,b,multiply(b,v))
| ~ product(u,a,b)
| ~ product(a,v,b)
| ~ product(b,v,multiply(b,v)) ),
inference(instantiation,[status(thm)],[c_1884]) ).
tcf(c_4802,plain,
( product(b,v,multiply(b,v))
| ~ defined(v)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_393]) ).
tcf(c_4924,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,v,X1)
| ~ product(b,v,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_inverse(b),X0,X1) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_8782,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,v)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,v,v)
| ~ product(multiplicative_identity,v,X0) ),
inference(instantiation,[status(thm)],[c_998]) ).
tcf(c_12340,plain,
( product(b,u,multiply(b,v))
| ~ product(u,a,b)
| ~ product(a,u,b)
| ~ product(u,b,multiply(b,v)) ),
inference(instantiation,[status(thm)],[c_1868]) ).
tcf(c_13722,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_91,c_92]) ).
tcf(c_13746,plain,
( defined(multiplicative_inverse(b))
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_100,c_300]) ).
tcf(c_13748,plain,
defined(multiplicative_inverse(b)),
inference(forward_subsumption_resolution,[status(thm)],[c_13746,c_110]) ).
tcf(c_14133,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,X2,X1)
| ~ product(u,X0,X2)
| ~ product(b,X0,X1) ),
inference(superposition,[status(thm)],[c_299,c_88]) ).
tcf(c_14399,plain,
! [X0: $i] :
( sum(additive_identity,b,additive_identity)
| product(a,X0,multiplicative_identity)
| ~ defined(b)
| ~ product(u,multiplicative_inverse(b),X0) ),
inference(superposition,[status(thm)],[c_13722,c_14133]) ).
tcf(c_14403,plain,
! [X0: $i] :
( product(a,X0,multiplicative_identity)
| ~ product(u,multiplicative_inverse(b),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14399,c_300,c_110]) ).
tcf(c_14418,plain,
( product(a,multiply(u,multiplicative_inverse(b)),multiplicative_identity)
| ~ defined(u)
| ~ defined(multiplicative_inverse(b)) ),
inference(superposition,[status(thm)],[c_102,c_14403]) ).
tcf(c_14421,plain,
product(a,multiply(u,multiplicative_inverse(b)),multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_14418,c_111,c_13748]) ).
tcf(c_14780,plain,
product(multiply(u,multiplicative_inverse(b)),a,multiplicative_identity),
inference(superposition,[status(thm)],[c_14421,c_92]) ).
tcf(c_15132,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiply(u,multiplicative_inverse(b)),X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_14780,c_88]) ).
tcf(c_17512,plain,
! [X0: $i] :
( product(multiplicative_identity,v,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(b,v,multiply(b,v))
| ~ product(multiplicative_inverse(b),multiply(b,v),X0) ),
inference(instantiation,[status(thm)],[c_4924]) ).
tcf(c_26596,plain,
! [X0: $i] :
( product(multiplicative_inverse(b),multiply(b,v),X0)
| ~ product(multiplicative_identity,u,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(b,u,multiply(b,v)) ),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_31547,plain,
! [X0: $i] :
( product(multiply(u,multiplicative_inverse(b)),b,X0)
| ~ product(multiplicative_identity,u,X0) ),
inference(superposition,[status(thm)],[c_299,c_15132]) ).
tcf(c_32962,plain,
! [X0: $i] : ~ product(multiplicative_identity,u,X0),
inference(global_subsumption_just,[status(thm)],[c_31547,c_112,c_110,c_99,c_115,c_114,c_116,c_113,c_302,c_305,c_994,c_3247,c_4048,c_4801,c_4802,c_8782,c_12340,c_17512,c_26596]) ).
tcf(c_32965,plain,
~ defined(u),
inference(superposition,[status(thm)],[c_90,c_32962]) ).
tcf(c_32968,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_32965,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD029-3 : 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 : n003.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 10:45:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.26/2.75 % SZS status Started for theBenchmark.p
% 10.26/2.75 % SZS status Unsatisfiable for theBenchmark.p
% 10.26/2.75
% 10.26/2.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.26/2.75
% 10.26/2.75 % ------ iProver source info
% 10.26/2.75
% 10.26/2.75 % git: date: 2026-07-19 20:42:38 +0200
% 10.26/2.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.26/2.75 % git: non_committed_changes: false
% 10.26/2.75
% 10.26/2.75 % ------ Parsing...% successful
% 10.26/2.75
% 10.26/2.75
% 10.26/2.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.26/2.75
% 10.26/2.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.26/2.75
% 10.26/2.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.26/2.75 % ------ Proving...
% 10.26/2.75 % ------ Problem Properties
% 10.26/2.75
% 10.26/2.75 %
% 10.26/2.75 % clauses 34
% 10.26/2.75 % conjectures 4
% 10.26/2.75 % EPR 26
% 10.26/2.75 % Horn 31
% 10.26/2.75 % unary 11
% 10.26/2.75 % binary 6
% 10.26/2.75 % lits 85
% 10.26/2.75 % lits eq 0
% 10.26/2.75 % fd_pure 0
% 10.26/2.75 % fd_pseudo 0
% 10.26/2.75 % fd_cond 0
% 10.26/2.75 % fd_pseudo_cond 0
% 10.26/2.75 % AC symbols 0
% 10.26/2.75
% 10.26/2.75 % ------ Schedule dynamic 5 is on
% 10.26/2.75
% 10.26/2.75 % ------ no equalities: superposition off
% 10.26/2.75
% 10.26/2.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.26/2.75
% 10.26/2.75
% 10.26/2.75 % ------
% 10.26/2.75 % Current options:
% 10.26/2.75 % ------
% 10.26/2.75
% 10.26/2.75
% 10.26/2.75 %
% 10.26/2.75
% 10.26/2.75 % ------ Proving...
% 10.26/2.75 %
% 10.26/2.75
% 10.26/2.75 % SZS status Unsatisfiable for theBenchmark.p
% 10.26/2.75
% 10.26/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.26/2.75
% 10.26/2.75
%------------------------------------------------------------------------------