%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 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 02:29:54 PM UTC 2026
% Result : Theorem 3.42s 1.27s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 168 ( 77 ~; 63 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 105 !; 15 ?; 48 :)
% 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(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_3) ).
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(f12,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) )
& id(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
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,X2] :
( ? [X4] :
( r3(X0,X2,X4)
& id(X4,X1) )
& ! [X3] :
( ~ r1(X3)
| ~ id(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(f20,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ? [X4] :
( r3(X0,X2,X4)
& id(X4,X1) )
& ! [X3] :
( ~ r1(X3)
| ~ id(X2,X3) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
! [X1,X2] :
( ! [X4] :
( ~ r3(X0,X2,X4)
| ~ id(X4,X1) )
| ? [X3] :
( r1(X3)
& id(X2,X3) ) ),
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(f24,plain,
! [X0,X1,X3] :
( ( ~ id(X3,sK2(X0,X1))
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,sK2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f26,plain,
! [X0,X1] :
( r3(X0,X1,sK7(X0,X1))
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& r2(X1,sK6(X0,X1))
& id(sK5(X0,X1),sK4(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f12]) ).
fof(f31,plain,
! [X1,X2] :
( ! [X4] :
( ~ r3(sK20,X2,X4)
| ~ id(X4,X1) )
| ( r1(sK21(X2))
& id(X2,sK21(X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X0,sK20),skolemize(X3,sK21(X2))],[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(f43,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| id(X3,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
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(f67,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f90,plain,
! [X2,X1,X4] :
( ~ r3(sK20,X2,X4)
| ~ id(X4,X1)
| r1(sK21(X2)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f91,plain,
! [X2,X1,X4] :
( ~ r3(sK20,X2,X4)
| ~ id(X4,X1)
| id(X2,sK21(X2)) ),
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_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(X2,sK2(X0,X1))
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
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_72,plain,
! [X0: $i,X1: $i] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f67]) ).
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,X1: $i,X2: $i] :
( id(X0,sK21(X0))
| ~ id(X1,X2)
| ~ r3(sK20,X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_92,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r1(sK21(X0))
| ~ id(X1,X2)
| ~ r3(sK20,X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_96,plain,
id(sK0,sK0),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_105,plain,
( r1(sK0)
| ~ id(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_122,plain,
( ~ r1(sK0)
| ~ r2(sK0,sK0)
| ~ id(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_427,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r1(sK21(X0))
| ~ id(X1,X2)
| ~ r3(sK20,X0,X1) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_428,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( id(X0,sK21(X0))
| ~ id(X1,X2)
| ~ r3(sK20,X0,X1) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_446,plain,
! [X0: $i] : r3(sK20,X0,sK7(sK20,X0)),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] :
( id(X0,sK21(X0))
| ~ id(sK7(sK20,X0),X1)
| ~ r3(sK20,X0,sK7(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i] :
( r1(sK21(X0))
| ~ id(sK7(sK20,X0),X1)
| ~ r3(sK20,X0,sK7(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i] :
( id(sK7(X0,X1),sK2(X0,X1))
| ~ r3(X0,X1,sK7(X0,X1)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_603,plain,
! [X0: $i] :
( r1(sK21(X0))
| ~ r3(sK20,X0,sK7(sK20,X0))
| ~ id(sK7(sK20,X0),sK7(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_448]) ).
tcf(c_604,plain,
! [X0: $i] : id(sK7(sK20,X0),sK7(sK20,X0)),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_803,plain,
! [X0: $i] :
( id(sK7(sK20,X0),sK2(sK20,X0))
| ~ r3(sK20,X0,sK7(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_471]) ).
tcf(c_804,plain,
! [X0: $i] :
( id(X0,sK21(X0))
| ~ r3(sK20,X0,sK7(sK20,X0))
| ~ id(sK7(sK20,X0),sK2(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_819,negated_conjecture,
! [X0: $i] : r1(sK21(X0)),
inference(global_subsumption_just,[status(thm)],[c_427,c_446,c_603,c_604]) ).
tcf(c_834,negated_conjecture,
! [X0: $i] : id(X0,sK21(X0)),
inference(global_subsumption_just,[status(thm)],[c_428,c_446,c_803,c_804]) ).
tcf(c_919,plain,
! [X0: $i] :
( id(sK0,X0)
| ~ r1(X0) ),
inference(superposition,[status(thm)],[c_49,c_58]) ).
tcf(c_923,plain,
! [X0: $i] : id(sK21(X0),X0),
inference(superposition,[status(thm)],[c_834,c_58]) ).
tcf(c_1080,plain,
! [X0: $i] :
( r2(X0,sK0)
| ~ r1(sK1(X0)) ),
inference(superposition,[status(thm)],[c_919,c_52]) ).
tcf(c_1305,plain,
! [X0: $i] :
( r1(X0)
| ~ r1(sK21(X0)) ),
inference(superposition,[status(thm)],[c_923,c_60]) ).
tcf(c_1310,plain,
! [X0: $i] : r1(X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1305,c_819]) ).
tcf(c_1311,plain,
! [X0: $i] : r2(X0,sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_1080,c_1310]) ).
tcf(c_1314,plain,
r2(sK0,sK0),
inference(instantiation,[status(thm)],[c_1311]) ).
tcf(c_1315,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1314,c_122,c_105,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n020.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 05:52:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 3.42/1.27 % SZS status Started for theBenchmark.p
% 3.42/1.27 % SZS status Theorem for theBenchmark.p
% 3.42/1.27
% 3.42/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.42/1.27
% 3.42/1.27 % ------ iProver source info
% 3.42/1.27
% 3.42/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.42/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.42/1.27 % git: non_committed_changes: false
% 3.42/1.27
% 3.42/1.27 % ------ Parsing...
% 3.42/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.42/1.27
% 3.42/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.42/1.27
% 3.42/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.42/1.27 % ------ Proving...
% 3.42/1.27 % ------ Problem Properties
% 3.42/1.27
% 3.42/1.27 %
% 3.42/1.27 % clauses 44
% 3.42/1.27 % conjectures 2
% 3.42/1.27 % EPR 15
% 3.42/1.27 % Horn 40
% 3.42/1.27 % unary 18
% 3.42/1.27 % binary 13
% 3.42/1.27 % lits 94
% 3.42/1.27 % lits eq 0
% 3.42/1.27 % fd_pure 0
% 3.42/1.27 % fd_pseudo 0
% 3.42/1.27 % fd_cond 0
% 3.42/1.27 % fd_pseudo_cond 0
% 3.42/1.27 % AC symbols 0
% 3.42/1.27
% 3.42/1.27 % ------ Schedule dynamic 5 is on
% 3.42/1.27
% 3.42/1.27 % ------ no equalities: superposition off
% 3.42/1.27
% 3.42/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.42/1.27
% 3.42/1.27
% 3.42/1.27 % ------
% 3.42/1.27 % Current options:
% 3.42/1.27 % ------
% 3.42/1.27
% 3.42/1.27
% 3.42/1.27 %
% 3.42/1.27
% 3.42/1.27 % ------ Proving...
% 3.42/1.27 %
% 3.42/1.27
% 3.42/1.27 % SZS status Theorem for theBenchmark.p
% 3.42/1.27
% 3.42/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.42/1.27
% 3.42/1.27
%------------------------------------------------------------------------------