%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN065+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 4.16s 1.17s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 67 ( 10 unt; 0 def)
% Number of atoms : 156 ( 70 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 54 ~; 73 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 100 ( 0 sgn 93 !; 7 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X1 = X0
& r1(X1) )
| ( X1 != X0
& ~ r1(X1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(f11,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X2 != X1
| ~ r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(f12,conjecture,
? [X0] :
( ! [X3] :
( X0 != X3
| ~ r1(X3) )
& ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nononesexist) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ! [X3] :
( X0 != X3
| ~ r1(X3) )
& ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ? [X3] :
( X0 = X3
& r1(X3) )
| ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( sK0 = X1
& r1(X1) )
| ( sK0 != X1
& ~ r1(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( sK1(X0) = X2
& r2(X0,X2) )
| ( sK1(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f24,plain,
! [X0] :
( ( sK22(X0) = X0
& r1(sK22(X0)) )
| ( sK20(X0) = X0
& r2(sK21(X0),sK20(X0))
& r1(sK21(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22]),skolemize(X1,sK20(X0)),skolemize(X2,sK21(X0)),skolemize(X3,sK22(X0))],[f14]) ).
fof(f26,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( sK0 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X0] :
( sK1(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0] :
( sK22(X0) = X0
| sK20(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0] :
( r1(sK22(X0))
| sK20(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0] :
( sK22(X0) = X0
| r2(sK21(X0),sK20(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
! [X0] :
( r1(sK22(X0))
| r2(sK21(X0),sK20(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
! [X0] :
( sK22(X0) = X0
| r1(sK21(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
! [X0] :
( r1(sK22(X0))
| r1(sK21(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f73,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f75,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f30]) ).
fof(f81,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f51]) ).
fof(f82,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ r1(X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f73]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( sK1(X0) = X1 )
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i] : r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f75]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_77,negated_conjecture,
! [X0: $i] :
( r1(sK22(X0))
| r1(sK21(X0)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_78,negated_conjecture,
! [X0: $i] :
( r1(sK21(X0))
| ( sK22(X0) = X0 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_79,negated_conjecture,
! [X0: $i] :
( r1(sK22(X0))
| r2(sK21(X0),sK20(X0)) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] :
( r2(sK21(X0),sK20(X0))
| ( sK22(X0) = X0 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_81,negated_conjecture,
! [X0: $i] :
( r1(sK22(X0))
| ( sK20(X0) = X0 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] :
( ( sK20(X0) = X0 )
| ( sK22(X0) = X0 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_501,negated_conjecture,
! [X0: $i] :
( ( sK20(X0) = X0 )
| ( sK22(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_502,negated_conjecture,
! [X0: $i] :
( r1(sK22(X0))
| ( sK20(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_503,negated_conjecture,
! [X0: $i] :
( r2(sK21(X0),sK20(X0))
| ( sK22(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_504,negated_conjecture,
! [X0: $i] :
( r1(sK22(X0))
| r2(sK21(X0),sK20(X0)) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_505,negated_conjecture,
! [X0: $i] :
( r1(sK21(X0))
| ( sK22(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_506,negated_conjecture,
! [X0: $i] :
( r1(sK22(X0))
| r1(sK21(X0)) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i] :
( r1(X0)
| ~ r1(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_791,plain,
! [X0: $i] :
( r2(sK21(X0),X0)
| ( sK22(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_501,c_503]) ).
tcf(c_807,plain,
! [X0: $i] :
( ( sK22(X0) = X0 )
| ( sK21(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_505,c_49]) ).
tcf(c_808,plain,
! [X0: $i] :
( r1(sK22(X0))
| ( sK21(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_506,c_49]) ).
tcf(c_809,plain,
! [X0: $i] :
( ( sK20(X0) = X0 )
| ( sK22(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_502,c_49]) ).
tcf(c_828,plain,
! [X0: $i] :
( ( sK22(X0) = sK0 )
| ( sK21(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_808,c_49]) ).
tcf(c_835,plain,
! [X0: $i] :
( r2(sK0,X0)
| ( sK22(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_807,c_791]) ).
tcf(c_857,plain,
! [X0: $i] :
( r1(sK22(X0))
| r2(sK21(X0),X0)
| ( sK22(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_809,c_504]) ).
tcf(c_870,plain,
! [X0: $i] :
( r2(sK21(X0),X0)
| ( sK22(X0) = sK0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_857,c_49]) ).
tcf(c_906,plain,
! [X0: $i] : ~ r1(sK1(X0)),
inference(superposition,[status(thm)],[c_52,c_76]) ).
tcf(c_954,plain,
! [X0: $i] :
( ( sK22(X0) = sK0 )
| ( sK1(sK21(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_870,c_51]) ).
tcf(c_956,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ( sK22(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_835,c_51]) ).
tcf(c_1092,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ( sK22(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_828,c_954]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i] :
( r1(sK1(X0))
| ~ r1(X1)
| ( sK1(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_510]) ).
tcf(c_2787,plain,
! [X0: $i] :
( r1(sK1(X0))
| ~ r1(sK0)
| ( sK1(X0) != sK0 ) ),
inference(instantiation,[status(thm)],[c_1181]) ).
tcf(c_3511,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ( sK1(sK0) = X0 ) ),
inference(superposition,[status(thm)],[c_1092,c_956]) ).
tcf(c_4150,plain,
! [X0: $i] :
( r2(X0,sK1(sK0))
| ( sK1(X0) = sK0 ) ),
inference(superposition,[status(thm)],[c_3511,c_52]) ).
tcf(c_4956,plain,
! [X0: $i] : r2(X0,sK1(sK0)),
inference(global_subsumption_just,[status(thm)],[c_4150,c_50,c_906,c_2787,c_4150]) ).
tcf(c_4963,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ r2(X0,sK1(sK0)) ),
inference(superposition,[status(thm)],[c_4956,c_65]) ).
tcf(c_4969,plain,
! [X0: $i,X1: $i] : X0 = X1,
inference(forward_subsumption_resolution,[status(thm)],[c_4963,c_4956]) ).
tcf(c_4997,plain,
! [X0: $i] : ~ r1(X0),
inference(superposition,[status(thm)],[c_4969,c_906]) ).
tcf(c_5000,plain,
! [X0: $i] : r1(X0),
inference(superposition,[status(thm)],[c_4969,c_50]) ).
tcf(c_5001,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4997,c_5000]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN065+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.35 % Computer : n015.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Thu Sep 24 05:55:11 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 4.16/1.17 % SZS status Started for theBenchmark.p
% 4.16/1.17 % SZS status Theorem for theBenchmark.p
% 4.16/1.17
% 4.16/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.16/1.17
% 4.16/1.17 % ------ iProver source info
% 4.16/1.17
% 4.16/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 4.16/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.16/1.17 % git: non_committed_changes: false
% 4.16/1.17
% 4.16/1.17 % ------ Parsing...
% 4.16/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.16/1.17
% 4.16/1.17 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 2 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.16/1.17
% 4.16/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.16/1.17
% 4.16/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.16/1.17 % ------ Proving...
% 4.16/1.17 % ------ Problem Properties
% 4.16/1.17
% 4.16/1.17 %
% 4.16/1.17 % clauses 30
% 4.16/1.17 % conjectures 6
% 4.16/1.17 % EPR 4
% 4.16/1.17 % Horn 20
% 4.16/1.17 % unary 16
% 4.16/1.17 % binary 13
% 4.16/1.17 % lits 45
% 4.16/1.17 % lits eq 20
% 4.16/1.17 % fd_pure 0
% 4.16/1.17 % fd_pseudo 0
% 4.16/1.17 % fd_cond 1
% 4.16/1.17 % fd_pseudo_cond 2
% 4.16/1.17 % AC symbols 0
% 4.16/1.17
% 4.16/1.17 % ------ Schedule dynamic 5 is on
% 4.16/1.17
% 4.16/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.16/1.17
% 4.16/1.17
% 4.16/1.17 % ------
% 4.16/1.17 % Current options:
% 4.16/1.17 % ------
% 4.16/1.17
% 4.16/1.17
% 4.16/1.17 %
% 4.16/1.17
% 4.16/1.17 % ------ Proving...
% 4.16/1.17 %
% 4.16/1.17
% 4.16/1.17 % SZS status Theorem for theBenchmark.p
% 4.16/1.17
% 4.16/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.16/1.17
% 4.16/1.17
%------------------------------------------------------------------------------