%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD050-4 : 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 01:15:47 PM UTC 2026
% Result : Unsatisfiable 1.22s 1.28s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 57 ( 37 unt; 2 def)
% Number of atoms : 112 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 40 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?; 29 :)
% 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(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f30,axiom,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
fof(f33,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
fof(f34,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
fof(f35,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_9) ).
fof(f36,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
fof(f37,negated_conjecture,
product(b,c,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_11) ).
fof(f38,negated_conjecture,
~ product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_12) ).
tcf(c_92,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_93,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_94,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_95,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_113,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_114,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_115,plain,
defined(c),
inference(cnf_transformation,[],[f29]) ).
tcf(c_116,plain,
defined(d),
inference(cnf_transformation,[],[f30]) ).
tcf(c_119,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f33]) ).
tcf(c_120,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(cnf_transformation,[],[f34]) ).
tcf(c_121,negated_conjecture,
product(a,multiplicative_inverse(b),s),
inference(cnf_transformation,[],[f35]) ).
tcf(c_122,negated_conjecture,
product(a,d,k),
inference(cnf_transformation,[],[f36]) ).
tcf(c_123,negated_conjecture,
product(b,c,k),
inference(cnf_transformation,[],[f37]) ).
tcf(c_124,negated_conjecture,
~ product(c,multiplicative_inverse(d),s),
inference(cnf_transformation,[],[f38]) ).
tcf(c_313,definition,
iPr_def_10 = multiplicative_inverse(d),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_314,definition,
iPr_def_11 = multiplicative_inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_315,negated_conjecture,
~ product(c,iPr_def_10,s),
inference(demodulation,[status(thm)],[c_124,c_313]) ).
tcf(c_316,negated_conjecture,
product(b,c,k),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_317,negated_conjecture,
product(a,d,k),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_318,negated_conjecture,
product(a,iPr_def_11,s),
inference(demodulation,[status(thm)],[c_121,c_314]) ).
tcf(c_319,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_320,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_825,plain,
product(d,a,k),
inference(superposition,[status(thm)],[c_317,c_96]) ).
tcf(c_828,plain,
product(iPr_def_11,a,s),
inference(superposition,[status(thm)],[c_318,c_96]) ).
tcf(c_887,plain,
( product(iPr_def_11,b,multiplicative_identity)
| sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_314,c_95]) ).
tcf(c_888,plain,
( product(iPr_def_10,d,multiplicative_identity)
| sum(additive_identity,d,additive_identity)
| ~ defined(d) ),
inference(superposition,[status(thm)],[c_313,c_95]) ).
tcf(c_890,plain,
product(iPr_def_10,d,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_888,c_319,c_116]) ).
tcf(c_891,plain,
product(iPr_def_11,b,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_887,c_320,c_114]) ).
tcf(c_1328,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(iPr_def_11,X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(b,X0,X1) ),
inference(superposition,[status(thm)],[c_891,c_92]) ).
tcf(c_1329,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(iPr_def_10,X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(d,X0,X1) ),
inference(superposition,[status(thm)],[c_890,c_92]) ).
tcf(c_1428,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,s)
| ~ product(iPr_def_11,X0,X2)
| ~ product(X0,X1,a) ),
inference(superposition,[status(thm)],[c_828,c_93]) ).
tcf(c_2176,plain,
! [X0: $i] :
( product(iPr_def_11,k,X0)
| ~ product(multiplicative_identity,c,X0) ),
inference(superposition,[status(thm)],[c_316,c_1328]) ).
tcf(c_2406,plain,
( product(iPr_def_11,k,c)
| ~ defined(c) ),
inference(superposition,[status(thm)],[c_94,c_2176]) ).
tcf(c_2408,plain,
product(iPr_def_11,k,c),
inference(forward_subsumption_resolution,[status(thm)],[c_2406,c_115]) ).
tcf(c_2462,plain,
! [X0: $i] :
( product(iPr_def_10,k,X0)
| ~ product(multiplicative_identity,a,X0) ),
inference(superposition,[status(thm)],[c_825,c_1329]) ).
tcf(c_2495,plain,
( product(iPr_def_10,k,a)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_94,c_2462]) ).
tcf(c_2498,plain,
product(iPr_def_10,k,a),
inference(forward_subsumption_resolution,[status(thm)],[c_2495,c_113]) ).
tcf(c_2609,plain,
! [X0: $i] :
( product(c,X0,s)
| ~ product(k,X0,a) ),
inference(superposition,[status(thm)],[c_2408,c_1428]) ).
tcf(c_2677,plain,
product(k,iPr_def_10,a),
inference(superposition,[status(thm)],[c_2498,c_96]) ).
tcf(c_5364,plain,
product(c,iPr_def_10,s),
inference(superposition,[status(thm)],[c_2677,c_2609]) ).
tcf(c_5365,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5364,c_315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 10:56:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.22/1.28 % SZS status Started for theBenchmark.p
% 1.22/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.22/1.28
% 1.22/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.22/1.28
% 1.22/1.28 % ------ iProver source info
% 1.22/1.28
% 1.22/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.22/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.22/1.28 % git: non_committed_changes: false
% 1.22/1.28
% 1.22/1.28 % ------ Parsing...% successful
% 1.22/1.28
% 1.22/1.28
% 1.22/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.22/1.28
% 1.22/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.22/1.28
% 1.22/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.22/1.28
% 1.22/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.22/1.28 % ------ Proving...
% 1.22/1.28 % ------ Problem Properties
% 1.22/1.28
% 1.22/1.28 %
% 1.22/1.28 % clauses 40
% 1.22/1.28 % conjectures 6
% 1.22/1.28 % EPR 30
% 1.22/1.28 % Horn 37
% 1.22/1.28 % unary 17
% 1.22/1.28 % binary 6
% 1.22/1.28 % lits 91
% 1.22/1.28 % lits eq 2
% 1.22/1.28 % fd_pure 0
% 1.22/1.28 % fd_pseudo 0
% 1.22/1.28 % fd_cond 0
% 1.22/1.28 % fd_pseudo_cond 0
% 1.22/1.28 % AC symbols 0
% 1.22/1.28
% 1.22/1.28 % ------ Schedule dynamic 5 is on
% 1.22/1.28
% 1.22/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.22/1.28
% 1.22/1.28
% 1.22/1.28 % ------
% 1.22/1.28 % Current options:
% 1.22/1.28 % ------
% 1.22/1.28
% 1.22/1.28
% 1.22/1.28 %
% 1.22/1.28
% 1.22/1.28 % ------ Proving...
% 1.22/1.28 %
% 1.22/1.28
% 1.22/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.22/1.28
% 1.22/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.22/1.28
% 1.22/1.28
%------------------------------------------------------------------------------