%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD049-3 : 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 : n017.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 26.86s 4.50s
% Output : CNFRefutation 26.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 78 ( 38 unt; 4 def)
% Number of atoms : 205 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 75 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 49 :)
% 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(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
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(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
fof(f32,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_6) ).
fof(f33,negated_conjecture,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
fof(f34,negated_conjecture,
~ product(a,d,multiply(b,c)),
file('/export/starexec/sandbox/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_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_109,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_110,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_111,plain,
defined(c),
inference(cnf_transformation,[],[f29]) ).
tcf(c_112,plain,
defined(d),
inference(cnf_transformation,[],[f30]) ).
tcf(c_113,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f31]) ).
tcf(c_114,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(cnf_transformation,[],[f32]) ).
tcf(c_115,negated_conjecture,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
inference(cnf_transformation,[],[f33]) ).
tcf(c_116,negated_conjecture,
~ product(a,d,multiply(b,c)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_297,definition,
iPr_def_10 = multiply(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_298,definition,
iPr_def_11 = multiplicative_inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_299,definition,
iPr_def_12 = multiplicative_inverse(d),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_300,definition,
iPr_def_13 = multiply(c,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_301,negated_conjecture,
~ product(a,d,iPr_def_10),
inference(demodulation,[status(thm)],[c_116,c_297]) ).
tcf(c_302,negated_conjecture,
product(a,iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_115,c_299,c_300,c_298]) ).
tcf(c_303,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_304,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_816,plain,
product(iPr_def_11,a,iPr_def_13),
inference(superposition,[status(thm)],[c_302,c_92]) ).
tcf(c_850,plain,
( defined(multiplicative_inverse(b))
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_100,c_304]) ).
tcf(c_851,plain,
( defined(multiplicative_inverse(d))
| ~ defined(d) ),
inference(superposition,[status(thm)],[c_100,c_303]) ).
tcf(c_853,plain,
( defined(iPr_def_12)
| ~ defined(d) ),
inference(light_normalisation,[status(thm)],[c_851,c_299]) ).
tcf(c_854,plain,
defined(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_853,c_112]) ).
tcf(c_855,plain,
( defined(iPr_def_11)
| ~ defined(b) ),
inference(light_normalisation,[status(thm)],[c_850,c_298]) ).
tcf(c_856,plain,
defined(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_855,c_110]) ).
tcf(c_873,plain,
( product(iPr_def_12,d,multiplicative_identity)
| sum(additive_identity,d,additive_identity)
| ~ defined(d) ),
inference(superposition,[status(thm)],[c_299,c_91]) ).
tcf(c_875,plain,
product(iPr_def_12,d,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_873,c_303,c_112]) ).
tcf(c_880,plain,
product(d,iPr_def_12,multiplicative_identity),
inference(superposition,[status(thm)],[c_875,c_92]) ).
tcf(c_910,plain,
( product(c,iPr_def_12,iPr_def_13)
| ~ defined(iPr_def_12)
| ~ defined(c) ),
inference(superposition,[status(thm)],[c_300,c_102]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_102,c_92]) ).
tcf(c_912,plain,
product(c,iPr_def_12,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_910,c_854,c_111]) ).
tcf(c_917,plain,
product(iPr_def_12,c,iPr_def_13),
inference(superposition,[status(thm)],[c_912,c_92]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(iPr_def_11,X1,X2)
| ~ product(iPr_def_13,X0,X2)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_816,c_88]) ).
tcf(c_1319,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(d,X2,X1)
| ~ product(iPr_def_12,X0,X2)
| ~ product(multiplicative_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_880,c_88]) ).
tcf(c_1393,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_1415,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,iPr_def_13)
| ~ product(a,X0,X2)
| ~ product(X0,X1,iPr_def_11) ),
inference(superposition,[status(thm)],[c_302,c_89]) ).
tcf(c_4275,plain,
( product(multiplicative_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_5783,plain,
! [X0: $i,X1: $i] :
( product(d,X1,X0)
| ~ defined(X0)
| ~ product(iPr_def_12,X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_1319]) ).
tcf(c_18659,plain,
( product(iPr_def_11,b,multiplicative_identity)
| sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_298,c_91]) ).
tcf(c_18663,plain,
product(iPr_def_11,b,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_18659,c_304,c_110]) ).
tcf(c_18668,plain,
product(b,iPr_def_11,multiplicative_identity),
inference(superposition,[status(thm)],[c_18663,c_92]) ).
tcf(c_18700,plain,
( product(b,c,iPr_def_10)
| ~ defined(c)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_297,c_102]) ).
tcf(c_18704,plain,
product(b,c,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_18700,c_111,c_110]) ).
tcf(c_19739,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,iPr_def_10)
| ~ product(b,X0,X2)
| ~ product(X0,X1,c) ),
inference(superposition,[status(thm)],[c_18704,c_89]) ).
tcf(c_20867,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,iPr_def_10)
| ~ product(iPr_def_11,X0,c) ),
inference(superposition,[status(thm)],[c_18668,c_19739]) ).
tcf(c_29985,plain,
! [X0: $i] :
( product(d,multiply(X0,iPr_def_12),X0)
| ~ defined(iPr_def_12)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_911,c_5783]) ).
tcf(c_29986,plain,
( product(d,iPr_def_13,c)
| ~ defined(c) ),
inference(superposition,[status(thm)],[c_917,c_5783]) ).
tcf(c_30033,plain,
product(d,iPr_def_13,c),
inference(forward_subsumption_resolution,[status(thm)],[c_29986,c_111]) ).
tcf(c_30041,plain,
! [X0: $i] :
( product(d,multiply(X0,iPr_def_12),X0)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29985,c_854]) ).
tcf(c_30397,plain,
product(iPr_def_13,d,c),
inference(superposition,[status(thm)],[c_30033,c_92]) ).
tcf(c_30497,plain,
! [X0: $i] :
( product(iPr_def_11,X0,c)
| ~ product(a,d,X0) ),
inference(superposition,[status(thm)],[c_30397,c_1315]) ).
tcf(c_38034,plain,
! [X0: $i] :
( product(X0,multiply(iPr_def_11,iPr_def_12),iPr_def_13)
| ~ defined(iPr_def_11)
| ~ product(a,d,X0) ),
inference(superposition,[status(thm)],[c_30041,c_1415]) ).
tcf(c_38046,plain,
! [X0: $i] :
( product(X0,multiply(iPr_def_11,iPr_def_12),iPr_def_13)
| ~ product(a,d,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38034,c_856]) ).
tcf(c_38498,plain,
! [X0: $i] :
( product(multiply(iPr_def_11,iPr_def_12),X0,iPr_def_13)
| ~ product(a,d,X0) ),
inference(superposition,[status(thm)],[c_38046,c_92]) ).
tcf(c_44979,plain,
! [X0: $i] :
( product(a,d,iPr_def_10)
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_identity,X0,iPr_def_10)
| ~ product(a,d,X0) ),
inference(instantiation,[status(thm)],[c_1393]) ).
tcf(c_46081,plain,
! [X0: $i] : ~ product(a,d,X0),
inference(global_subsumption_just,[status(thm)],[c_38498,c_109,c_301,c_4275,c_20867,c_30497,c_44979]) ).
tcf(c_46084,plain,
( ~ defined(d)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_102,c_46081]) ).
tcf(c_46087,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_46084,c_112,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD049-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 10:48:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 0.15/0.46
% 0.15/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.46
% 0.15/0.46 % Detected problem language: tptp
% 0.15/0.48 % Proving...
% 26.86/4.50 % SZS status Started for theBenchmark.p
% 26.86/4.50 % SZS status Unsatisfiable for theBenchmark.p
% 26.86/4.50
% 26.86/4.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.86/4.50
% 26.86/4.50 % ------ iProver source info
% 26.86/4.50
% 26.86/4.50 % git: date: 2026-07-19 20:42:38 +0200
% 26.86/4.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.86/4.50 % git: non_committed_changes: false
% 26.86/4.50
% 26.86/4.50 % ------ Parsing...% successful
% 26.86/4.50
% 26.86/4.50
% 26.86/4.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.86/4.50
% 26.86/4.50 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 26.86/4.50
% 26.86/4.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.86/4.50
% 26.86/4.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.86/4.50 % ------ Proving...
% 26.86/4.50 % ------ Problem Properties
% 26.86/4.50
% 26.86/4.50 %
% 26.86/4.50 % clauses 38
% 26.86/4.50 % conjectures 4
% 26.86/4.50 % EPR 26
% 26.86/4.50 % Horn 35
% 26.86/4.50 % unary 15
% 26.86/4.50 % binary 6
% 26.86/4.50 % lits 89
% 26.86/4.50 % lits eq 4
% 26.86/4.50 % fd_pure 0
% 26.86/4.50 % fd_pseudo 0
% 26.86/4.50 % fd_cond 0
% 26.86/4.50 % fd_pseudo_cond 0
% 26.86/4.50 % AC symbols 0
% 26.86/4.50
% 26.86/4.50 % ------ Schedule dynamic 5 is on
% 26.86/4.50
% 26.86/4.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 26.86/4.50
% 26.86/4.50
% 26.86/4.50 % ------
% 26.86/4.50 % Current options:
% 26.86/4.50 % ------
% 26.86/4.50
% 26.86/4.50
% 26.86/4.50 %
% 26.86/4.50
% 26.86/4.50 % ------ Proving...
% 26.86/4.50 %
% 26.86/4.50
% 26.86/4.50 % SZS status Unsatisfiable for theBenchmark.p
% 26.86/4.50
% 26.86/4.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.87/4.50
% 26.87/4.50
%------------------------------------------------------------------------------