%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD031-1 : 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 : n020.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 01:15:42 PM UTC 2026
% Result : Unsatisfiable 2.78s 1.19s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 20 unt; 1 def)
% Number of atoms : 113 ( 1 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 81 ( 41 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f22,axiom,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
equalish(a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_multiplicative_identity_2) ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
fof(f31,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_not_equal) ).
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_101,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
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,negated_conjecture,
equalish(a,multiplicative_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_109,negated_conjecture,
~ equalish(a,additive_identity),
inference(cnf_transformation,[],[f30]) ).
tcf(c_110,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
inference(cnf_transformation,[],[f31]) ).
tcf(c_283,definition,
iPr_def_10 = multiplicative_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_284,negated_conjecture,
~ equalish(iPr_def_10,multiplicative_identity),
inference(demodulation,[status(thm)],[c_110,c_283]) ).
tcf(c_285,negated_conjecture,
~ equalish(a,additive_identity),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_286,negated_conjecture,
equalish(a,multiplicative_identity),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_723,plain,
equalish(multiplicative_identity,a),
inference(superposition,[status(thm)],[c_286,c_101]) ).
tcf(c_772,plain,
( defined(multiplicative_inverse(a))
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_94,c_285]) ).
tcf(c_774,plain,
( defined(iPr_def_10)
| ~ defined(a) ),
inference(light_normalisation,[status(thm)],[c_772,c_283]) ).
tcf(c_775,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_774,c_107]) ).
tcf(c_841,plain,
! [X0: $i] :
( equalish(multiplicative_identity,X0)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_723,c_102]) ).
tcf(c_990,plain,
( equalish(iPr_def_10,multiplicative_identity)
| ~ equalish(multiplicative_identity,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_999,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(superposition,[status(thm)],[c_286,c_841]) ).
tcf(c_1094,plain,
( equalish(a,additive_identity)
| equalish(multiply(a,iPr_def_10),multiplicative_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_283,c_86]) ).
tcf(c_1098,plain,
equalish(multiply(a,iPr_def_10),multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_1094,c_285,c_107]) ).
tcf(c_1248,plain,
! [X0: $i] :
( equalish(multiply(a,iPr_def_10),X0)
| ~ equalish(multiplicative_identity,X0) ),
inference(superposition,[status(thm)],[c_1098,c_102]) ).
tcf(c_1249,plain,
equalish(multiplicative_identity,multiply(a,iPr_def_10)),
inference(superposition,[status(thm)],[c_1098,c_101]) ).
tcf(c_1292,plain,
! [X0: $i] :
( equalish(multiplicative_identity,X0)
| ~ equalish(multiply(a,iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_1249,c_102]) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i] :
( equalish(multiply(a,iPr_def_10),X1)
| ~ equalish(multiplicative_identity,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_1248,c_102]) ).
tcf(c_2097,plain,
! [X0: $i] :
( equalish(multiplicative_identity,multiply(X0,iPr_def_10))
| ~ defined(iPr_def_10)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_104,c_1292]) ).
tcf(c_2108,plain,
! [X0: $i] :
( equalish(multiplicative_identity,multiply(X0,iPr_def_10))
| ~ equalish(a,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2097,c_775]) ).
tcf(c_5621,plain,
! [X0: $i] :
( equalish(multiply(a,iPr_def_10),multiply(X0,iPr_def_10))
| ~ equalish(multiplicative_identity,multiplicative_identity)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_2108,c_1353]) ).
tcf(c_5634,plain,
! [X0: $i] :
( equalish(multiply(a,iPr_def_10),multiply(X0,iPr_def_10))
| ~ equalish(a,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5621,c_999]) ).
tcf(c_5888,plain,
! [X0: $i,X1: $i] :
( equalish(multiply(a,iPr_def_10),X1)
| ~ equalish(a,X0)
| ~ equalish(multiply(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_5634,c_102]) ).
tcf(c_6022,plain,
( equalish(multiply(a,iPr_def_10),iPr_def_10)
| ~ defined(iPr_def_10)
| ~ equalish(a,multiplicative_identity) ),
inference(superposition,[status(thm)],[c_85,c_5888]) ).
tcf(c_6047,plain,
equalish(multiply(a,iPr_def_10),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6022,c_775,c_286]) ).
tcf(c_6092,plain,
equalish(multiplicative_identity,iPr_def_10),
inference(superposition,[status(thm)],[c_6047,c_1292]) ).
tcf(c_6098,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6092,c_990,c_284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD031-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.35 % Computer : n020.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 10:45:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.78/1.19 % SZS status Started for theBenchmark.p
% 2.78/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.78/1.19
% 2.78/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.78/1.19
% 2.78/1.19 % ------ iProver source info
% 2.78/1.19
% 2.78/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 2.78/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.78/1.19 % git: non_committed_changes: false
% 2.78/1.19
% 2.78/1.19 % ------ Parsing...% successful
% 2.78/1.19
% 2.78/1.19
% 2.78/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.78/1.19
% 2.78/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.78/1.19
% 2.78/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.78/1.19
% 2.78/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.78/1.19 % ------ Proving...
% 2.78/1.19 % ------ Problem Properties
% 2.78/1.19
% 2.78/1.19 %
% 2.78/1.19 % clauses 32
% 2.78/1.19 % conjectures 3
% 2.78/1.19 % EPR 14
% 2.78/1.19 % Horn 29
% 2.78/1.19 % unary 8
% 2.78/1.19 % binary 6
% 2.78/1.19 % lits 78
% 2.78/1.19 % lits eq 1
% 2.78/1.19 % fd_pure 0
% 2.78/1.19 % fd_pseudo 0
% 2.78/1.19 % fd_cond 0
% 2.78/1.19 % fd_pseudo_cond 0
% 2.78/1.19 % AC symbols 0
% 2.78/1.19
% 2.78/1.19 % ------ Schedule dynamic 5 is on
% 2.78/1.19
% 2.78/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.78/1.19
% 2.78/1.19
% 2.78/1.19 % ------
% 2.78/1.19 % Current options:
% 2.78/1.19 % ------
% 2.78/1.19
% 2.78/1.19
% 2.78/1.19 %
% 2.78/1.19
% 2.78/1.19 % ------ Proving...
% 2.78/1.19 %
% 2.78/1.19
% 2.78/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.78/1.19
% 2.78/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.78/1.19
% 2.78/1.19
%------------------------------------------------------------------------------