%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN067+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:29:55 PM UTC 2026
% Result : Theorem 2.71s 1.49s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 90 ( 45 ~; 33 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 59 ( 0 sgn 54 !; 5 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f18,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( ~ r1(X2)
| ~ id(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(f19,conjecture,
? [X0] :
! [X1] :
( ~ r1(X1)
| ~ id(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosexistid) ).
fof(f20,negated_conjecture,
~ ? [X0] :
! [X1] :
( ~ r1(X1)
| ~ id(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
? [X1] :
( r1(X1)
& id(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X1] :
( ( ~ id(X1,sK0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f23,plain,
! [X0,X2] :
( ( ~ id(X2,sK1(X0))
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f31,plain,
! [X0] :
( r1(sK20(X0))
& id(X0,sK20(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f21]) ).
fof(f32,plain,
! [X1] :
( ~ id(X1,sK0)
| r1(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X1] :
( ~ r1(X1)
| id(X1,sK0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0] :
( ~ id(X2,sK1(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f48,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0,X1] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f90,plain,
! [X0] : r1(sK20(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f91,plain,
! [X0] : id(X0,sK20(X0)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_49,plain,
! [X0: $i] :
( id(X0,sK0)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i] :
( r1(X0)
| ~ id(X0,sK0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( r2(X1,X0)
| ~ id(X0,sK1(X1)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i] : id(X0,X0),
inference(cnf_transformation,[],[f48]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X0)
| ~ r2(X2,X1)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_91,negated_conjecture,
! [X0: $i] : id(X0,sK20(X0)),
inference(cnf_transformation,[],[f91]) ).
tcf(c_92,negated_conjecture,
! [X0: $i] : r1(sK20(X0)),
inference(cnf_transformation,[],[f90]) ).
tcf(c_97,plain,
id(sK0,sK0),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_107,plain,
( r1(sK0)
| ~ id(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_124,plain,
( ~ r1(sK0)
| ~ r2(sK0,sK0)
| ~ id(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_417,negated_conjecture,
! [X0: $i] : r1(sK20(X0)),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_418,negated_conjecture,
! [X0: $i] : id(X0,sK20(X0)),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_847,plain,
! [X0: $i] :
( id(sK0,X0)
| ~ r1(X0) ),
inference(superposition,[status(thm)],[c_49,c_58]) ).
tcf(c_851,plain,
! [X0: $i] : id(sK20(X0),X0),
inference(superposition,[status(thm)],[c_418,c_58]) ).
tcf(c_1042,plain,
! [X0: $i] :
( r2(X0,sK0)
| ~ r1(sK1(X0)) ),
inference(superposition,[status(thm)],[c_847,c_52]) ).
tcf(c_1240,plain,
! [X0: $i] :
( r1(X0)
| ~ r1(sK20(X0)) ),
inference(superposition,[status(thm)],[c_851,c_60]) ).
tcf(c_1245,plain,
! [X0: $i] : r1(X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1240,c_417]) ).
tcf(c_1246,plain,
! [X0: $i] : r2(X0,sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_1042,c_1245]) ).
tcf(c_1249,plain,
r2(sK0,sK0),
inference(instantiation,[status(thm)],[c_1246]) ).
tcf(c_1250,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1249,c_124,c_107,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN067+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n020.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 05:52:35 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.10/0.63
% 0.10/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63
% 0.15/0.63 % Detected problem language: tptp
% 0.15/0.64 % Proving...
% 2.71/1.49 % SZS status Started for theBenchmark.p
% 2.71/1.49 % SZS status Theorem for theBenchmark.p
% 2.71/1.49
% 2.71/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.71/1.49
% 2.71/1.49 % ------ iProver source info
% 2.71/1.49
% 2.71/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.71/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.71/1.49 % git: non_committed_changes: false
% 2.71/1.49
% 2.71/1.49 % ------ Parsing...
% 2.71/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.71/1.49
% 2.71/1.49 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.71/1.49
% 2.71/1.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.71/1.49 % ------ Proving...
% 2.71/1.49 % ------ Problem Properties
% 2.71/1.49
% 2.71/1.49 %
% 2.71/1.49 % clauses 44
% 2.71/1.49 % conjectures 2
% 2.71/1.49 % EPR 15
% 2.71/1.49 % Horn 40
% 2.71/1.49 % unary 20
% 2.71/1.49 % binary 13
% 2.71/1.49 % lits 90
% 2.71/1.49 % lits eq 0
% 2.71/1.49 % fd_pure 0
% 2.71/1.49 % fd_pseudo 0
% 2.71/1.49 % fd_cond 0
% 2.71/1.49 % fd_pseudo_cond 0
% 2.71/1.49 % AC symbols 0
% 2.71/1.49
% 2.71/1.49 % ------ Schedule dynamic 5 is on
% 2.71/1.49
% 2.71/1.49 % ------ no equalities: superposition off
% 2.71/1.49
% 2.71/1.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.71/1.49
% 2.71/1.49
% 2.71/1.49 % ------
% 2.71/1.49 % Current options:
% 2.71/1.49 % ------
% 2.71/1.49
% 2.71/1.49
% 2.71/1.49 %
% 2.71/1.49
% 2.71/1.49 % ------ Proving...
% 2.71/1.49 %
% 2.71/1.49
% 2.71/1.49 % SZS status Theorem for theBenchmark.p
% 2.71/1.49
% 2.71/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.71/1.49
% 2.71/1.49
%------------------------------------------------------------------------------