%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN070+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 : n017.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 02:29:56 PM UTC 2026
% Result : Theorem 3.76s 1.28s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 128 ( 56 ~; 44 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 61 !; 19 ?; 33 :)
% 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(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f13,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r4(X0,X1,X5)
& r3(X5,X0,X2) )
& ? [X3] :
( ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) )
& id(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(f19,conjecture,
? [X0] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& id(X0,X4) )
& ? [X1] :
( ? [X3] :
( r2(X3,X1)
& r1(X3) )
& ? [X2] :
( r3(X1,X2,X0)
& r1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onepluszeroidone) ).
fof(f20,negated_conjecture,
~ ? [X0] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& id(X0,X4) )
& ? [X1] :
( ? [X3] :
( r2(X3,X1)
& r1(X3) )
& ? [X2] :
( r3(X1,X2,X0)
& r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
( ! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ r1(X5) )
| ~ id(X0,X4) )
| ! [X1] :
( ! [X3] :
( ~ r2(X3,X1)
| ~ r1(X3) )
| ! [X2] :
( ~ r3(X1,X2,X0)
| ~ r1(X2) ) ) ),
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(f27,plain,
! [X0,X1] :
( r4(X0,X1,sK11(X0,X1))
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& r2(X1,sK10(X0,X1))
& id(sK9(X0,X1),sK8(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f13]) ).
fof(f28,plain,
! [X0] :
( r3(X0,sK13(X0),sK12(X0))
& r1(sK13(X0))
& id(sK12(X0),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f15]) ).
fof(f31,plain,
! [X1] :
( ~ id(X1,sK0)
| r1(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f74,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f78,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f79,plain,
! [X0] : id(sK12(X0),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ id(X0,X4)
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X1,X2,X0)
| ~ r1(X2) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i] :
( r1(X0)
| ~ id(X0,sK0) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,plain,
! [X0: $i] : id(X0,X0),
inference(cnf_transformation,[],[f47]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : r2(X0,sK10(X1,X0)),
inference(cnf_transformation,[],[f74]) ).
tcf(c_79,plain,
! [X0: $i] : id(sK12(X0),X0),
inference(cnf_transformation,[],[f79]) ).
tcf(c_80,plain,
! [X0: $i] : r1(sK13(X0)),
inference(cnf_transformation,[],[f78]) ).
tcf(c_81,plain,
! [X0: $i] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f77]) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r1(X4)
| ~ r1(X1)
| ~ r2(X5,X3)
| ~ r2(X4,X0)
| ~ id(X2,X3)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_95,plain,
id(sK0,sK0),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_98,plain,
r2(sK0,sK10(sK0,sK0)),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_104,plain,
( r1(sK0)
| ~ id(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_426,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r1(X4)
| ~ r1(X1)
| ~ r2(X5,X3)
| ~ r2(X4,X0)
| ~ id(X2,X3)
| ~ r3(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X2)
| ~ r1(sK13(X0))
| ~ r2(X3,X1)
| ~ r2(X2,X0)
| ~ id(sK12(X0),X1) ),
inference(superposition,[status(thm)],[c_81,c_426]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X2)
| ~ r2(X3,X1)
| ~ r2(X2,X0)
| ~ id(sK12(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_896,c_80]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_79,c_897]) ).
tcf(c_1125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(X0)
| ~ r2(X0,sK10(X1,X2)) ),
inference(superposition,[status(thm)],[c_74,c_997]) ).
tcf(c_1132,plain,
( ~ r1(sK0)
| ~ r2(sK0,sK10(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_1125]) ).
tcf(c_1133,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1132,c_104,c_98,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN070+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.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 05:48:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.76/1.28 % SZS status Started for theBenchmark.p
% 3.76/1.28 % SZS status Theorem for theBenchmark.p
% 3.76/1.28
% 3.76/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.76/1.28
% 3.76/1.28 % ------ iProver source info
% 3.76/1.28
% 3.76/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.76/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.76/1.28 % git: non_committed_changes: false
% 3.76/1.28
% 3.76/1.28 % ------ Parsing...
% 3.76/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.76/1.28
% 3.76/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.76/1.28
% 3.76/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.76/1.28 % ------ Proving...
% 3.76/1.28 % ------ Problem Properties
% 3.76/1.28
% 3.76/1.28 %
% 3.76/1.28 % clauses 43
% 3.76/1.28 % conjectures 1
% 3.76/1.28 % EPR 16
% 3.76/1.28 % Horn 39
% 3.76/1.28 % unary 18
% 3.76/1.28 % binary 13
% 3.76/1.28 % lits 95
% 3.76/1.28 % lits eq 0
% 3.76/1.28 % fd_pure 0
% 3.76/1.28 % fd_pseudo 0
% 3.76/1.28 % fd_cond 0
% 3.76/1.28 % fd_pseudo_cond 0
% 3.76/1.28 % AC symbols 0
% 3.76/1.28
% 3.76/1.28 % ------ Schedule dynamic 5 is on
% 3.76/1.28
% 3.76/1.28 % ------ no equalities: superposition off
% 3.76/1.28
% 3.76/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.76/1.28
% 3.76/1.28
% 3.76/1.28 % ------
% 3.76/1.28 % Current options:
% 3.76/1.28 % ------
% 3.76/1.28
% 3.76/1.28
% 3.76/1.28 %
% 3.76/1.28
% 3.76/1.28 % ------ Proving...
% 3.76/1.28 %
% 3.76/1.28
% 3.76/1.28 % SZS status Theorem for theBenchmark.p
% 3.76/1.28
% 3.76/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/1.28
% 3.76/1.28
%------------------------------------------------------------------------------