%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM190-1 : 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 : n010.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 02:23:28 PM UTC 2026
% Result : Unsatisfiable 3.56s 1.72s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 17 unt; 3 def)
% Number of atoms : 89 ( 21 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 44 ( 20 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f53,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
fof(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f176,negated_conjecture,
omega = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_omega_is_not_null_1) ).
fof(f177,plain,
null_class = omega,
inference(reorient_equations,[],[f176]) ).
fof(f210,plain,
! [X0] :
( member(omega,X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f48,f177]) ).
fof(f223,plain,
! [X0] :
( omega = intersection(X0,regular(X0))
| omega = X0 ),
inference(definition_unfolding,[],[f70,f177,f177]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_243,negated_conjecture,
! [X0: $i] :
( member(omega,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_246,plain,
inductive(omega),
inference(cnf_transformation,[],[f51]) ).
tcf(c_248,plain,
member(omega,universal_class),
inference(cnf_transformation,[],[f53]) ).
tcf(c_261,negated_conjecture,
! [X0: $i] :
( ( X0 = omega )
| ( intersection(X0,regular(X0)) = omega ) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_564,plain,
! [X0: $i] :
( member(omega,X0)
| ~ inductive(X0) ),
inference(prop_impl_just,[status(thm)],[c_243]) ).
tcf(c_2166,plain,
! [X0: $i] :
( member(omega,X0)
| ( X0 != omega ) ),
inference(resolution_lifted,[status(thm)],[c_564,c_246]) ).
tcf(c_2167,plain,
member(omega,omega),
inference(unflattening,[status(thm)],[c_2166]) ).
tcf(c_4614,definition,
iPr_def_10 = unordered_pair(omega,omega),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4615,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4623,definition,
iPr_def_19 = intersection(iPr_def_11,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_4633,negated_conjecture,
! [X0: $i] :
( ( X0 = omega )
| ( intersection(X0,regular(X0)) = omega ) ),
inference(demodulation,[status(thm)],[c_261]) ).
tcf(c_6505,plain,
( member(omega,iPr_def_10)
| ~ member(omega,universal_class) ),
inference(superposition,[status(thm)],[c_4614,c_216]) ).
tcf(c_6506,plain,
member(omega,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6505,c_248]) ).
tcf(c_6520,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = omega )
| ~ member(X0,omega) ),
inference(superposition,[status(thm)],[c_4633,c_226]) ).
tcf(c_6522,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_4623,c_226]) ).
tcf(c_6670,plain,
! [X0: $i] :
( member(omega,X0)
| ( X0 = omega ) ),
inference(superposition,[status(thm)],[c_2167,c_6520]) ).
tcf(c_6993,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4615,c_229]) ).
tcf(c_7217,plain,
( member(omega,iPr_def_11)
| ( omega = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_6670,c_6522]) ).
tcf(c_12247,plain,
( ( omega = iPr_def_19 )
| ~ member(omega,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7217,c_6993]) ).
tcf(c_12248,plain,
omega = iPr_def_19,
inference(forward_subsumption_resolution,[status(thm)],[c_12247,c_6506]) ).
tcf(c_12331,plain,
member(iPr_def_19,iPr_def_10),
inference(demodulation,[status(thm)],[c_6506,c_12248]) ).
tcf(c_12370,plain,
member(iPr_def_19,iPr_def_19),
inference(demodulation,[status(thm)],[c_2167,c_12248]) ).
tcf(c_13003,plain,
member(iPr_def_19,iPr_def_11),
inference(superposition,[status(thm)],[c_12370,c_6522]) ).
tcf(c_13007,plain,
~ member(iPr_def_19,iPr_def_10),
inference(superposition,[status(thm)],[c_13003,c_6993]) ).
tcf(c_13008,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13007,c_12331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 03:10:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.56/1.72 % SZS status Started for theBenchmark.p
% 3.56/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 3.56/1.72
% 3.56/1.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/1.72
% 3.56/1.72 % ------ iProver source info
% 3.56/1.72
% 3.56/1.72 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/1.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/1.72 % git: non_committed_changes: false
% 3.56/1.72
% 3.56/1.72 % ------ Parsing...% successful
% 3.56/1.72
% 3.56/1.72
% 3.56/1.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/1.72
% 3.56/1.72 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.56/1.72
% 3.56/1.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/1.72
% 3.56/1.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.56/1.72 % ------ Proving...
% 3.56/1.72 % ------ Problem Properties
% 3.56/1.72
% 3.56/1.72 %
% 3.56/1.72 % clauses 125
% 3.56/1.72 % conjectures 11
% 3.56/1.72 % EPR 15
% 3.56/1.72 % Horn 113
% 3.56/1.72 % unary 36
% 3.56/1.72 % binary 58
% 3.56/1.73 % lits 259
% 3.56/1.73 % lits eq 50
% 3.56/1.73 % fd_pure 0
% 3.56/1.73 % fd_pseudo 0
% 3.56/1.73 % fd_cond 5
% 3.56/1.73 % fd_pseudo_cond 10
% 3.56/1.73 % AC symbols 0
% 3.56/1.73
% 3.56/1.73 % ------ Schedule dynamic 5 is on
% 3.56/1.73
% 3.56/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.56/1.73
% 3.56/1.73
% 3.56/1.73 % ------
% 3.56/1.73 % Current options:
% 3.56/1.73 % ------
% 3.56/1.73
% 3.56/1.73
% 3.56/1.73 %
% 3.56/1.73
% 3.56/1.73 % ------ Proving...
% 3.56/1.73 %
% 3.56/1.73
% 3.56/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.56/1.73
% 3.56/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.73
% 3.56/1.73
%------------------------------------------------------------------------------