%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN059+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 : n008.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 02:29:53 PM UTC 2026
% Result : Theorem 4.06s 1.30s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 27 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 186 ( 84 ~; 74 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 128 ( 0 sgn 108 !; 20 ?; 46 :)
% 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(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(f10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r3(X3,X4,X5)
& r3(X0,X1,X2) )
| ( ~ r3(X3,X4,X5)
& ~ r3(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_10) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r4(X3,X4,X5)
& r4(X0,X1,X2) )
| ( ~ r4(X3,X4,X5)
& ~ r4(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_11) ).
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(f16,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( r1(X3)
& id(X1,X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(f19,conjecture,
? [X0,X1,X2,X3] :
( ? [X5] :
( ? [X6] :
( r3(X6,X5,X3)
& r4(X0,X0,X6) )
& r4(X1,X1,X5) )
& ? [X4] :
( r4(X2,X2,X4)
& id(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwoid) ).
fof(f20,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( ? [X5] :
( ? [X6] :
( r3(X6,X5,X3)
& r4(X0,X0,X6) )
& r4(X1,X1,X5) )
& ? [X4] :
( r4(X2,X2,X4)
& id(X3,X4) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ! [X5] :
( ! [X6] :
( ~ r3(X6,X5,X3)
| ~ r4(X0,X0,X6) )
| ~ r4(X1,X1,X5) )
| ! [X4] :
( ~ r4(X2,X2,X4)
| ~ id(X3,X4) ) ),
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(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(f29,plain,
! [X0] :
( r1(sK16(X0))
& id(sK14(X0),sK16(X0))
& r4(X0,sK15(X0),sK14(X0))
& r1(sK15(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f16]) ).
fof(f34,plain,
! [X1] :
( ~ r1(X1)
| id(X1,sK0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f60,plain,
! [X2,X3,X0,X1,X4,X5] :
( r3(X3,X4,X5)
| ~ r3(X0,X1,X2)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4,X5] :
( r4(X3,X4,X5)
| ~ r4(X0,X1,X2)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
inference(cnf_transformation,[],[f11]) ).
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(f80,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f81,plain,
! [X0] : id(sK14(X0),sK16(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f82,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f83,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r3(X6,X5,X3)
| ~ r4(X0,X0,X6)
| ~ r4(X1,X1,X5)
| ~ r4(X2,X2,X4)
| ~ id(X3,X4) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i] :
( id(X0,sK0)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i] : id(X0,X0),
inference(cnf_transformation,[],[f47]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r3(X5,X3,X4)
| ~ id(X2,X4)
| ~ id(X1,X3)
| ~ id(X0,X5)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r4(X5,X3,X4)
| ~ id(X2,X4)
| ~ id(X1,X3)
| ~ id(X0,X5)
| ~ r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
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_82,plain,
! [X0: $i] : r1(sK15(X0)),
inference(cnf_transformation,[],[f83]) ).
tcf(c_83,plain,
! [X0: $i] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f82]) ).
tcf(c_84,plain,
! [X0: $i] : id(sK14(X0),sK16(X0)),
inference(cnf_transformation,[],[f81]) ).
tcf(c_85,plain,
! [X0: $i] : r1(sK16(X0)),
inference(cnf_transformation,[],[f80]) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ id(X2,X5)
| ~ r4(X6,X6,X0)
| ~ r4(X4,X4,X5)
| ~ r4(X3,X3,X1)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_93,plain,
r1(sK15(sK0)),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_94,plain,
r1(sK13(sK0)),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_95,plain,
id(sK0,sK0),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_96,plain,
id(sK12(sK0),sK0),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_100,plain,
r4(sK0,sK15(sK0),sK14(sK0)),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_101,plain,
r3(sK0,sK13(sK0),sK12(sK0)),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_122,plain,
( ~ id(sK0,sK0)
| ~ r4(sK0,sK0,sK0)
| ~ r3(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r3(X3,X2,X1)
| ~ id(X0,X3)
| ~ id(sK13(X0),X2)
| ~ id(sK12(X0),X1)
| ~ r3(X0,sK13(X0),sK12(X0)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_499,plain,
( r3(sK0,sK0,sK0)
| ~ id(sK0,sK0)
| ~ id(sK13(sK0),sK0)
| ~ id(sK12(sK0),sK0)
| ~ r3(sK0,sK13(sK0),sK12(sK0)) ),
inference(instantiation,[status(thm)],[c_498]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r4(X3,X1,X2)
| ~ id(X0,X3)
| ~ id(sK14(X0),X2)
| ~ id(sK15(X0),X1)
| ~ r4(X0,sK15(X0),sK14(X0)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_513,plain,
( r4(sK0,sK0,sK0)
| ~ id(sK0,sK0)
| ~ id(sK14(sK0),sK0)
| ~ id(sK15(sK0),sK0)
| ~ r4(sK0,sK15(sK0),sK14(sK0)) ),
inference(instantiation,[status(thm)],[c_512]) ).
tcf(c_1045,plain,
! [X0: $i] : id(sK16(X0),sK14(X0)),
inference(superposition,[status(thm)],[c_84,c_58]) ).
tcf(c_1068,plain,
! [X0: $i] :
( id(sK13(X0),sK0)
| ~ r1(sK13(X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1069,plain,
( id(sK13(sK0),sK0)
| ~ r1(sK13(sK0)) ),
inference(instantiation,[status(thm)],[c_1068]) ).
tcf(c_1129,plain,
! [X0: $i] :
( id(sK15(X0),sK0)
| ~ r1(sK15(X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1130,plain,
( id(sK15(sK0),sK0)
| ~ r1(sK15(sK0)) ),
inference(instantiation,[status(thm)],[c_1129]) ).
tcf(c_1872,plain,
! [X0: $i] :
( id(sK14(X0),sK0)
| ~ r1(sK14(X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1873,plain,
( id(sK14(sK0),sK0)
| ~ r1(sK14(sK0)) ),
inference(instantiation,[status(thm)],[c_1872]) ).
tcf(c_2046,plain,
! [X0: $i] :
( r1(sK14(X0))
| ~ r1(sK16(X0)) ),
inference(superposition,[status(thm)],[c_1045,c_60]) ).
tcf(c_2055,plain,
! [X0: $i] : r1(sK14(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2046,c_85]) ).
tcf(c_2088,plain,
r1(sK14(sK0)),
inference(instantiation,[status(thm)],[c_2055]) ).
tcf(c_2089,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2088,c_1873,c_1130,c_1069,c_513,c_499,c_122,c_101,c_100,c_96,c_95,c_94,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN059+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 : n008.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 05:51:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 4.06/1.30 % SZS status Started for theBenchmark.p
% 4.06/1.30 % SZS status Theorem for theBenchmark.p
% 4.06/1.30
% 4.06/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.06/1.30
% 4.06/1.30 % ------ iProver source info
% 4.06/1.30
% 4.06/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.06/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.06/1.30 % git: non_committed_changes: false
% 4.06/1.30
% 4.06/1.30 % ------ Parsing...
% 4.06/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.06/1.30
% 4.06/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.06/1.30
% 4.06/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.06/1.30 % ------ Proving...
% 4.06/1.30 % ------ Problem Properties
% 4.06/1.30
% 4.06/1.30 %
% 4.06/1.30 % clauses 43
% 4.06/1.30 % conjectures 1
% 4.06/1.30 % EPR 16
% 4.06/1.30 % Horn 39
% 4.06/1.30 % unary 18
% 4.06/1.30 % binary 13
% 4.06/1.30 % lits 93
% 4.06/1.30 % lits eq 0
% 4.06/1.30 % fd_pure 0
% 4.06/1.30 % fd_pseudo 0
% 4.06/1.30 % fd_cond 0
% 4.06/1.30 % fd_pseudo_cond 0
% 4.06/1.30 % AC symbols 0
% 4.06/1.30
% 4.06/1.30 % ------ Schedule dynamic 5 is on
% 4.06/1.30
% 4.06/1.30 % ------ no equalities: superposition off
% 4.06/1.30
% 4.06/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.06/1.30
% 4.06/1.30
% 4.06/1.30 % ------
% 4.06/1.30 % Current options:
% 4.06/1.30 % ------
% 4.06/1.30
% 4.06/1.30
% 4.06/1.30 %
% 4.06/1.30
% 4.06/1.30 % ------ Proving...
% 4.06/1.30 %
% 4.06/1.30
% 4.06/1.30 % SZS status Theorem for theBenchmark.p
% 4.06/1.30
% 4.06/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.06/1.30
% 4.06/1.30
%------------------------------------------------------------------------------