%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN066+2 : 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 : n004.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 4.75s 1.30s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 11 unt; 0 def)
% Number of atoms : 180 ( 71 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 183 ( 76 ~; 89 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 101 ( 0 sgn 93 !; 8 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X1 = X0
& r1(X1) )
| ( X1 != X0
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( X2 = X1
& r2(X0,X2) )
| ( X2 != X1
& ~ r2(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X3 != X2
| ~ r2(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(f11,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X2 != X1
| ~ r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(f12,conjecture,
? [X0] :
( ! [X4] :
( X0 != X4
| ~ r1(X4) )
& ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerononetwoexist) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ! [X4] :
( X0 != X4
| ~ r1(X4) )
& ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ? [X4] :
( X0 = X4
& r1(X4) )
| ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0] :
( ( sK3(X0) = X0
& r1(sK3(X0)) )
| ( sK0(X0) = X0
& r2(sK1(X0),sK0(X0))
& r2(sK2(X0),sK1(X0))
& r1(sK2(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0)),skolemize(X3,sK2(X0)),skolemize(X4,sK3(X0))],[f14]) ).
fof(f18,plain,
! [X1] :
( ( sK9 = X1
& r1(X1) )
| ( sK9 != X1
& ~ r1(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f1]) ).
fof(f19,plain,
! [X0,X2] :
( ( sK10(X0) = X2
& r2(X0,X2) )
| ( sK10(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f2]) ).
fof(f25,plain,
! [X0] :
( sK3(X0) = X0
| sK0(X0) = X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0] :
( r1(sK3(X0))
| sK0(X0) = X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0] :
( sK3(X0) = X0
| r2(sK1(X0),sK0(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0] :
( r1(sK3(X0))
| r2(sK1(X0),sK0(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0] :
( sK3(X0) = X0
| r2(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0] :
( r1(sK3(X0))
| r2(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X0] :
( r1(sK3(X0))
| r1(sK2(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X1] :
( r1(X1)
| sK9 != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X1] :
( sK9 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f47,plain,
! [X2,X0] :
( r2(X0,X2)
| sK10(X0) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f48,plain,
! [X2,X0] :
( sK10(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f75,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f33]) ).
fof(f76,plain,
r1(sK9),
inference(equality_resolution,[],[f42]) ).
fof(f78,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f45]) ).
fof(f79,plain,
! [X0] : r2(X0,sK10(X0)),
inference(equality_resolution,[],[f47]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( r1(sK3(X0))
| r1(sK2(X0)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( r1(sK3(X0))
| r2(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( r2(sK2(X0),sK1(X0))
| ( sK3(X0) = X0 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( r1(sK3(X0))
| r2(sK1(X0),sK0(X0)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( r2(sK1(X0),sK0(X0))
| ( sK3(X0) = X0 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( r1(sK3(X0))
| ( sK0(X0) = X0 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( ( sK0(X0) = X0 )
| ( sK3(X0) = X0 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( X0 = sK9 )
| ~ r1(X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,plain,
r1(sK9),
inference(cnf_transformation,[],[f76]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( sK10(X0) = X1 )
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_69,plain,
! [X0: $i] : r2(X0,sK10(X0)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_88,plain,
r2(sK9,sK10(sK9)),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_100,plain,
( ( sK9 = sK9 )
| ~ r1(sK9) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_101,plain,
( ~ r1(sK9)
| ~ r2(sK9,sK9) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i] :
( r1(X0)
| ~ r1(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2(X0,X2)
| ~ r2(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_846,plain,
! [X0: $i] :
( r2(sK1(X0),X0)
| ( sK3(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_54]) ).
tcf(c_859,plain,
! [X0: $i] :
( ( sK3(X0) = X0 )
| ~ r1(sK1(X0)) ),
inference(superposition,[status(thm)],[c_52,c_57]) ).
tcf(c_863,plain,
! [X0: $i] : ~ r1(sK10(X0)),
inference(superposition,[status(thm)],[c_69,c_57]) ).
tcf(c_877,plain,
~ r1(sK10(sK9)),
inference(instantiation,[status(thm)],[c_863]) ).
tcf(c_944,plain,
! [X0: $i] :
( r1(sK3(X0))
| ( sK2(X0) = sK9 ) ),
inference(superposition,[status(thm)],[c_49,c_65]) ).
tcf(c_995,plain,
! [X0: $i] :
( ( sK3(X0) = sK9 )
| ( sK2(X0) = sK9 ) ),
inference(superposition,[status(thm)],[c_944,c_65]) ).
tcf(c_1063,plain,
! [X0: $i] :
( r1(sK3(X0))
| r2(sK9,sK1(X0))
| ( sK3(X0) = sK9 ) ),
inference(superposition,[status(thm)],[c_995,c_51]) ).
tcf(c_1163,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ r2(X0,sK10(X1)) ),
inference(superposition,[status(thm)],[c_69,c_67]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2(X0,X2)
| ~ r2(X1,sK10(X1))
| ( X2 != sK10(X1) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_547]) ).
tcf(c_1206,plain,
( r2(sK9,sK9)
| ~ r2(sK9,sK10(sK9))
| ( sK9 != sK9 )
| ( sK9 != sK10(sK9) ) ),
inference(instantiation,[status(thm)],[c_1205]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i] :
( r1(sK10(X0))
| ~ r1(X1)
| ( sK10(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_546]) ).
tcf(c_1242,plain,
( r1(sK10(sK9))
| ~ r1(sK9)
| ( sK10(sK9) != sK9 ) ),
inference(instantiation,[status(thm)],[c_1241]) ).
tcf(c_1246,plain,
! [X0: $i] :
( r2(sK9,sK1(X0))
| ( sK3(X0) = sK9 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1063,c_65]) ).
tcf(c_1254,plain,
! [X0: $i] :
( ( sK1(X0) = sK10(sK9) )
| ( sK3(X0) = sK9 ) ),
inference(superposition,[status(thm)],[c_1246,c_68]) ).
tcf(c_1585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sK10(X0) )
| ~ r2(X2,X1)
| ~ r2(sK10(X0),X1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1810,plain,
! [X0: $i] :
( ( sK1(sK10(X0)) = X0 )
| ( sK3(sK10(X0)) = sK10(X0) ) ),
inference(superposition,[status(thm)],[c_846,c_1163]) ).
tcf(c_2943,plain,
! [X0: $i] :
( ( sK3(sK10(X0)) = sK10(X0) )
| ~ r1(X0) ),
inference(superposition,[status(thm)],[c_1810,c_859]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK10(X0) )
| ~ r2(X1,sK10(X1))
| ~ r2(sK10(X0),sK10(X1)) ),
inference(instantiation,[status(thm)],[c_1585]) ).
tcf(c_3803,plain,
( ( sK9 = sK10(sK9) )
| ~ r2(sK9,sK10(sK9))
| ~ r2(sK10(sK9),sK10(sK9)) ),
inference(instantiation,[status(thm)],[c_3802]) ).
tcf(c_3838,plain,
sK3(sK10(sK9)) = sK10(sK9),
inference(superposition,[status(thm)],[c_66,c_2943]) ).
tcf(c_4355,plain,
( r1(sK10(sK9))
| ( sK0(sK10(sK9)) = sK10(sK9) ) ),
inference(superposition,[status(thm)],[c_3838,c_55]) ).
tcf(c_4357,plain,
sK0(sK10(sK9)) = sK10(sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_4355,c_863]) ).
tcf(c_4374,plain,
( r1(sK3(sK10(sK9)))
| r2(sK1(sK10(sK9)),sK10(sK9)) ),
inference(superposition,[status(thm)],[c_4357,c_53]) ).
tcf(c_4379,plain,
( r1(sK10(sK9))
| r2(sK1(sK10(sK9)),sK10(sK9)) ),
inference(light_normalisation,[status(thm)],[c_4374,c_3838]) ).
tcf(c_4380,plain,
r2(sK1(sK10(sK9)),sK10(sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_4379,c_863]) ).
tcf(c_4422,plain,
( r2(sK10(sK9),sK10(sK9))
| ( sK3(sK10(sK9)) = sK9 ) ),
inference(superposition,[status(thm)],[c_1254,c_4380]) ).
tcf(c_4437,plain,
( r2(sK10(sK9),sK10(sK9))
| ( sK10(sK9) = sK9 ) ),
inference(light_normalisation,[status(thm)],[c_4422,c_3838]) ).
tcf(c_4441,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4437,c_3803,c_1242,c_1206,c_877,c_101,c_100,c_88,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN066+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 05:51:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 4.75/1.30 % SZS status Started for theBenchmark.p
% 4.75/1.30 % SZS status Theorem for theBenchmark.p
% 4.75/1.30
% 4.75/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.75/1.30
% 4.75/1.30 % ------ iProver source info
% 4.75/1.30
% 4.75/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.75/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.75/1.30 % git: non_committed_changes: false
% 4.75/1.30
% 4.75/1.30 % ------ Parsing...
% 4.75/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.75/1.30
% 4.75/1.30 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 5 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.75/1.30
% 4.75/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.75/1.30
% 4.75/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.75/1.30 % ------ Proving...
% 4.75/1.30 % ------ Problem Properties
% 4.75/1.30
% 4.75/1.30 %
% 4.75/1.30 % clauses 32
% 4.75/1.30 % conjectures 8
% 4.75/1.30 % EPR 4
% 4.75/1.30 % Horn 20
% 4.75/1.30 % unary 16
% 4.75/1.30 % binary 15
% 4.75/1.30 % lits 49
% 4.75/1.30 % lits eq 21
% 4.75/1.30 % fd_pure 0
% 4.75/1.30 % fd_pseudo 0
% 4.75/1.30 % fd_cond 1
% 4.75/1.30 % fd_pseudo_cond 2
% 4.75/1.30 % AC symbols 0
% 4.75/1.30
% 4.75/1.30 % ------ Schedule dynamic 5 is on
% 4.75/1.30
% 4.75/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.75/1.30
% 4.75/1.30
% 4.75/1.30 % ------
% 4.75/1.30 % Current options:
% 4.75/1.30 % ------
% 4.75/1.30
% 4.75/1.30
% 4.75/1.30 %
% 4.75/1.30
% 4.75/1.30 % ------ Proving...
% 4.75/1.30 %
% 4.75/1.30
% 4.75/1.30 % SZS status Theorem for theBenchmark.p
% 4.75/1.30
% 4.75/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.75/1.30
% 4.75/1.30
%------------------------------------------------------------------------------