%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN062+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 : n006.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 2.44s 6.29s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 77 ( 33 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 44 ~; 32 |; 14 &)
% ( 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 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 68 !; 10 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
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(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r3(X0,X1,X3) )
| ( X3 != X2
& ~ r3(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
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] :
? [X1,X2] :
( ? [X4] :
( X4 = X1
& r3(X0,X2,X4) )
& ! [X3] :
( X2 != X3
| ~ r1(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbers) ).
fof(f13,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ? [X4] :
( X4 = X1
& r3(X0,X2,X4) )
& ! [X3] :
( X2 != X3
| ~ r1(X3) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
! [X1,X2] :
( ! [X4] :
( X1 != X4
| ~ r3(X0,X2,X4) )
| ? [X3] :
( X2 = X3
& r1(X3) ) ),
inference(ennf_transformation,[],[f13]) ).
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(f17,plain,
! [X0,X1,X3] :
( ( sK2(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK2(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f24,plain,
! [X1,X2] :
( ! [X4] :
( X1 != X4
| ~ r3(sK20,X2,X4) )
| ( sK21(X2) = X2
& r1(sK21(X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X0,sK20),skolemize(X3,sK21(X2))],[f14]) ).
fof(f30,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X3,X0,X1] :
( r3(X0,X1,X3)
| sK2(X0,X1) != X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
! [X2,X1,X4] :
( X1 != X4
| ~ r3(sK20,X2,X4)
| sK21(X2) = X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X2,X1,X4] :
( X1 != X4
| ~ r3(sK20,X2,X4)
| r1(sK21(X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f71,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f30]) ).
fof(f73,plain,
! [X0,X1] : r3(X0,X1,sK2(X0,X1)),
inference(equality_resolution,[],[f34]) ).
fof(f78,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f79,plain,
! [X2,X4] :
( ~ r3(sK20,X2,X4)
| r1(sK21(X2)) ),
inference(equality_resolution,[],[f65]) ).
fof(f80,plain,
! [X2,X4] :
( ~ r3(sK20,X2,X4)
| sK21(X2) = X2 ),
inference(equality_resolution,[],[f64]) ).
tcf(c_52,plain,
! [X0: $i] : r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f71]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : r3(X0,X1,sK2(X0,X1)),
inference(cnf_transformation,[],[f73]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i] :
( r1(sK21(X0))
| ~ r3(sK20,X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_78,negated_conjecture,
! [X0: $i,X1: $i] :
( ( sK21(X0) = X0 )
| ~ r3(sK20,X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK21(X3) = X3 )
| ( X1 != X3 )
| ( X0 != sK20 )
| ( sK2(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_78]) ).
tcf(c_301,plain,
! [X0: $i] : sK21(X0) = X0,
inference(unflattening,[status(thm)],[c_300]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r1(sK21(X3))
| ( X1 != X3 )
| ( X0 != sK20 )
| ( sK2(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_77]) ).
tcf(c_307,plain,
! [X0: $i] : r1(sK21(X0)),
inference(unflattening,[status(thm)],[c_306]) ).
tcf(c_512,plain,
! [X0: $i] : r1(X0),
inference(demodulation,[status(thm)],[c_307,c_301]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i] : ~ r2(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[c_76,c_512]) ).
tcf(c_514,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 05:53:01 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.44/6.29 % SZS status Started for theBenchmark.p
% 2.44/6.29 % SZS status Theorem for theBenchmark.p
% 2.44/6.29
% 2.44/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.44/6.29
% 2.44/6.29 % ------ iProver source info
% 2.44/6.29
% 2.44/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.44/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.44/6.29 % git: non_committed_changes: false
% 2.44/6.29
% 2.44/6.29 % ------ Parsing...
% 2.44/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.44/6.29
% 2.44/6.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 2.44/6.29
% 2.44/6.29 % SZS status Theorem for theBenchmark.p
% 2.44/6.29
% 2.44/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.44/6.29
% 2.44/6.29
%------------------------------------------------------------------------------