%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN081+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 : n026.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 02:29:59 PM UTC 2026
% Result : Theorem 3.00s 1.18s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 91 ( 21 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 115 ( 54 ~; 39 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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; 0-1 aty)
% Number of variables : 83 ( 0 sgn 65 !; 18 ?; 31 :)
% 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(f8,axiom,
! [X0] :
? [X1] :
( X1 = X0
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r2(X4,X3) )
& X2 = X3 )
& r3(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplusyeqthree) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r2(X4,X3) )
& X2 = X3 )
& r3(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) )
| ~ r2(X5,X4) )
| ~ r2(X4,X3) )
| X2 != X3 )
| ~ r3(X0,X1,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(f21,plain,
! [X0] :
( sK12(X0) = X0
& r3(X0,sK13(X0),sK12(X0))
& r1(sK13(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
fof(f25,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| X2 != X3
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X0,X1,X3) ),
inference(equality_resolution,[],[f63]) ).
tcf(c_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i] : r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f69]) ).
tcf(c_67,plain,
! [X0: $i] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_68,plain,
! [X0: $i] : sK12(X0) = X0,
inference(cnf_transformation,[],[f51]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_193,plain,
! [X0: $i] : r3(X0,sK13(X0),X0),
inference(light_normalisation,[status(thm)],[c_67,c_68]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ r1(X6)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ( X1 != X3 )
| ( X0 != X1 )
| ( sK13(X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_193]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(unflattening,[status(thm)],[c_351]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(demodulation,[status(thm)],[c_352]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_865]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i] :
( ~ r1(X0)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_1095]) ).
tcf(c_1112,plain,
! [X0: $i] : ~ r1(X0),
inference(superposition,[status(thm)],[c_52,c_1105]) ).
tcf(c_1113,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_1112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 06:00:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 3.00/1.18 % SZS status Started for theBenchmark.p
% 3.00/1.18 % SZS status Theorem for theBenchmark.p
% 3.00/1.18
% 3.00/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.00/1.18
% 3.00/1.18 % ------ iProver source info
% 3.00/1.18
% 3.00/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.00/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.00/1.18 % git: non_committed_changes: false
% 3.00/1.18
% 3.00/1.18 % ------ Parsing...
% 3.00/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.00/1.18
% 3.00/1.18 % ------ 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 %
% 3.00/1.18
% 3.00/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.00/1.18
% 3.00/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.00/1.18 % ------ Proving...
% 3.00/1.18 % ------ Problem Properties
% 3.00/1.18
% 3.00/1.18 %
% 3.00/1.18 % clauses 25
% 3.00/1.18 % conjectures 0
% 3.00/1.18 % EPR 5
% 3.00/1.18 % Horn 21
% 3.00/1.18 % unary 16
% 3.00/1.18 % binary 7
% 3.00/1.18 % lits 37
% 3.00/1.18 % lits eq 15
% 3.00/1.18 % fd_pure 0
% 3.00/1.18 % fd_pseudo 0
% 3.00/1.18 % fd_cond 1
% 3.00/1.18 % fd_pseudo_cond 2
% 3.00/1.18 % AC symbols 0
% 3.00/1.18
% 3.00/1.18 % ------ Schedule dynamic 5 is on
% 3.00/1.18
% 3.00/1.18 % ------ no conjectures: strip conj schedule
% 3.00/1.18
% 3.00/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.00/1.18
% 3.00/1.18
% 3.00/1.18 % ------
% 3.00/1.18 % Current options:
% 3.00/1.18 % ------
% 3.00/1.18
% 3.00/1.18
% 3.00/1.18 %
% 3.00/1.18
% 3.00/1.18 % ------ Proving...
% 3.00/1.18 %
% 3.00/1.18
% 3.00/1.18 % SZS status Theorem for theBenchmark.p
% 3.00/1.18
% 3.00/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.00/1.18
% 3.00/1.18
%------------------------------------------------------------------------------