%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN087+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 : n013.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 02:30:00 PM UTC 2026
% Result : Theorem 2.76s 1.30s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 71 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 77 ( 37 ~; 24 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 34 !; 10 ?; 15 :)
% 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(f9,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( X1 = X3
& r1(X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(f12,conjecture,
? [X0] :
( ? [X2] :
( X0 = X2
& r1(X2) )
& ? [X1] :
( r4(X1,X1,X0)
& r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerotimeszeroeqzero) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X2] :
( X0 = X2
& r1(X2) )
& ? [X1] :
( r4(X1,X1,X0)
& r1(X1) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X2] :
( X0 != X2
| ~ r1(X2) )
| ! [X1] :
( ~ r4(X1,X1,X0)
| ~ r1(X1) ) ),
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(f22,plain,
! [X0] :
( sK14(X0) = sK16(X0)
& r1(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))],[f9]) ).
fof(f25,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( sK0 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f54,plain,
! [X0] : sK14(X0) = sK16(X0),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X0,X1] :
( X0 != X2
| ~ r1(X2)
| ~ r4(X1,X1,X0)
| ~ r1(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f66,plain,
! [X0] : r4(X0,sK15(X0),sK16(X0)),
inference(definition_unfolding,[],[f56,f54]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f77,plain,
! [X2,X1] :
( ~ r1(X2)
| ~ r4(X1,X1,X2)
| ~ r1(X1) ),
inference(equality_resolution,[],[f63]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ r1(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f67]) ).
tcf(c_69,plain,
! [X0: $i] : r1(sK15(X0)),
inference(cnf_transformation,[],[f57]) ).
tcf(c_70,plain,
! [X0: $i] : r4(X0,sK15(X0),sK16(X0)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_71,plain,
! [X0: $i] : r1(sK16(X0)),
inference(cnf_transformation,[],[f55]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r1(X0)
| ~ r4(X0,X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(X1)
| ( X0 != X1 )
| ( sK16(X0) != X2 )
| ( sK15(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_77]) ).
tcf(c_326,plain,
! [X0: $i] :
( ~ r1(X0)
| ~ r1(sK16(X0))
| ( sK15(X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_325]) ).
tcf(c_328,plain,
! [X0: $i] :
( ~ r1(X0)
| ( sK15(X0) != X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_326,c_71,c_326]) ).
tcf(c_628,plain,
! [X0: $i] :
( ~ r1(X0)
| ( sK15(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_328]) ).
tcf(c_886,plain,
! [X0: $i] : sK15(X0) = sK0,
inference(superposition,[status(thm)],[c_69,c_49]) ).
tcf(c_890,plain,
! [X0: $i] :
( ~ r1(X0)
| ( X0 != sK0 ) ),
inference(demodulation,[status(thm)],[c_628,c_886]) ).
tcf(c_893,plain,
! [X0: $i] : ~ r1(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_890]) ).
tcf(c_894,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 06:00:07 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.76/1.30 % SZS status Started for theBenchmark.p
% 2.76/1.30 % SZS status Theorem for theBenchmark.p
% 2.76/1.30
% 2.76/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.76/1.30
% 2.76/1.30 % ------ iProver source info
% 2.76/1.30
% 2.76/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.76/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.76/1.30 % git: non_committed_changes: false
% 2.76/1.30
% 2.76/1.30 % ------ Parsing...
% 2.76/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.76/1.30
% 2.76/1.30 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 4 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.76/1.30
% 2.76/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.76/1.30
% 2.76/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.76/1.30 % ------ Proving...
% 2.76/1.30 % ------ Problem Properties
% 2.76/1.30
% 2.76/1.30 %
% 2.76/1.30 % clauses 27
% 2.76/1.30 % conjectures 0
% 2.76/1.30 % EPR 4
% 2.76/1.30 % Horn 23
% 2.76/1.30 % unary 16
% 2.76/1.30 % binary 9
% 2.76/1.30 % lits 40
% 2.76/1.30 % lits eq 17
% 2.76/1.30 % fd_pure 0
% 2.76/1.30 % fd_pseudo 0
% 2.76/1.30 % fd_cond 1
% 2.76/1.30 % fd_pseudo_cond 2
% 2.76/1.30 % AC symbols 0
% 2.76/1.30
% 2.76/1.30 % ------ Schedule dynamic 5 is on
% 2.76/1.30
% 2.76/1.30 % ------ no conjectures: strip conj schedule
% 2.76/1.30
% 2.76/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.76/1.30
% 2.76/1.30
% 2.76/1.30 % ------
% 2.76/1.30 % Current options:
% 2.76/1.30 % ------
% 2.76/1.30
% 2.76/1.30
% 2.76/1.30 %
% 2.76/1.30
% 2.76/1.30 % ------ Proving...
% 2.76/1.30 %
% 2.76/1.30
% 2.76/1.30 % SZS status Theorem for theBenchmark.p
% 2.76/1.30
% 2.76/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.76/1.30
% 2.76/1.30
%------------------------------------------------------------------------------