%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN073+1 : 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 : 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 02:29:57 PM UTC 2026
% Result : Theorem 4.38s 1.44s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 17 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 101 ~; 84 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 100 ( 0 sgn 93 !; 7 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( r2(X2,X3)
& r2(X0,X1) )
| ( ~ r2(X2,X3)
& ~ r2(X0,X1) )
| ~ id(X1,X3)
| ~ id(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_9) ).
fof(f14,axiom,
! [X0,X1] :
( id(X0,X1)
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( ~ r2(X0,X3)
| ~ id(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_3a) ).
fof(f18,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( ~ r1(X2)
| ~ id(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(f19,conjecture,
! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( ~ id(X1,X0)
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneunidtwo) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( ~ id(X1,X0)
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
( ? [X3] :
( r2(X3,X0)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) )
& ? [X1] :
( id(X1,X0)
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
( r2(sK3,sK0)
& r2(sK4,sK3)
& r1(sK4)
& id(sK1,sK0)
& r2(sK2,sK1)
& r1(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f21]) ).
fof(f25,plain,
! [X1] :
( ( ~ id(X1,sK10)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,sK10) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f1]) ).
fof(f26,plain,
! [X0,X2] :
( ( ~ id(X2,sK11(X0))
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,sK11(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f2]) ).
fof(f32,plain,
r2(sK3,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
r2(sK4,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
id(sK1,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
r2(sK2,sK1),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
r1(sK2),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f40,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X1] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f53,plain,
! [X1] :
( ~ id(X1,sK10)
| r1(X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X1] :
( ~ r1(X1)
| id(X1,sK10) ),
inference(cnf_transformation,[],[f25]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( id(X0,X1)
| ~ r2(X1,X2)
| ~ r2(X0,X3)
| ~ id(X3,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( r2(X2,X3)
| ~ r2(X0,X1)
| ~ id(X1,X3)
| ~ id(X0,X2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f62,plain,
! [X2,X0] :
( ~ id(X2,sK11(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f65,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| id(X2,sK11(X0)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,negated_conjecture,
r1(sK2),
inference(cnf_transformation,[],[f37]) ).
tcf(c_50,negated_conjecture,
r2(sK2,sK1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_51,negated_conjecture,
id(sK1,sK0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,negated_conjecture,
r2(sK4,sK3),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,negated_conjecture,
r2(sK3,sK0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i] : id(X0,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ id(X2,X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_68,plain,
! [X0: $i] :
( id(X0,sK10)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_69,plain,
! [X0: $i] :
( r1(X0)
| ~ id(X0,sK10) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( id(X0,X2)
| ~ id(X1,X3)
| ~ r2(X2,X3)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2(X2,X3)
| ~ id(X1,X3)
| ~ id(X0,X2)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( id(X1,sK11(X0))
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( r2(X1,X0)
| ~ id(X0,sK11(X1)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_100,plain,
id(sK0,sK0),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_432,plain,
( id(sK2,sK10)
| ~ r1(sK2) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] :
( ~ r1(sK2)
| ~ id(sK2,X1)
| ~ r2(X0,X1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i,X2: $i] :
( id(X0,sK10)
| ~ r2(sK10,X2)
| ~ id(X1,X2)
| ~ r2(X0,X1) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( r2(X0,X1)
| ~ r2(sK2,sK1)
| ~ id(sK1,X1)
| ~ id(sK2,X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_660,plain,
! [X0: $i] :
( ~ r1(sK2)
| ~ id(sK2,sK10)
| ~ r2(X0,sK10) ),
inference(instantiation,[status(thm)],[c_487]) ).
tcf(c_685,plain,
! [X0: $i] :
( r2(sK10,X0)
| ~ id(sK2,sK10)
| ~ r2(sK2,sK1)
| ~ id(sK1,X0) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_686,plain,
( r2(sK10,sK0)
| ~ id(sK1,sK0)
| ~ id(sK2,sK10)
| ~ r2(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_685]) ).
tcf(c_887,plain,
! [X0: $i] :
( id(sK10,X0)
| ~ r1(X0) ),
inference(superposition,[status(thm)],[c_68,c_56]) ).
tcf(c_1142,plain,
! [X0: $i] :
( r2(X0,sK10)
| ~ r1(sK11(X0)) ),
inference(superposition,[status(thm)],[c_887,c_74]) ).
tcf(c_1200,plain,
! [X0: $i] : ~ r1(sK11(X0)),
inference(global_subsumption_just,[status(thm)],[c_1142,c_49,c_432,c_660,c_1142]) ).
tcf(c_1253,plain,
! [X0: $i] :
( id(sK3,sK10)
| ~ r2(sK3,sK0)
| ~ id(sK0,X0)
| ~ r2(sK10,X0) ),
inference(instantiation,[status(thm)],[c_525]) ).
tcf(c_1254,plain,
( id(sK3,sK10)
| ~ id(sK0,sK0)
| ~ r2(sK10,sK0)
| ~ r2(sK3,sK0) ),
inference(instantiation,[status(thm)],[c_1253]) ).
tcf(c_1385,plain,
! [X0: $i,X1: $i] :
( r1(sK11(X0))
| ~ r1(X1)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_73,c_66]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r2(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1385,c_1200]) ).
tcf(c_1673,plain,
~ r1(sK3),
inference(superposition,[status(thm)],[c_53,c_1426]) ).
tcf(c_2132,plain,
( r1(sK3)
| ~ id(sK3,sK10) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2133,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2132,c_1673,c_1254,c_686,c_432,c_100,c_50,c_51,c_54,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 05:58:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.46 % Proving...
% 4.38/1.44 % SZS status Started for theBenchmark.p
% 4.38/1.44 % SZS status Theorem for theBenchmark.p
% 4.38/1.44
% 4.38/1.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.38/1.44
% 4.38/1.44 % ------ iProver source info
% 4.38/1.44
% 4.38/1.44 % git: date: 2026-07-19 20:42:38 +0200
% 4.38/1.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.38/1.44 % git: non_committed_changes: false
% 4.38/1.44
% 4.38/1.44 % ------ Parsing...
% 4.38/1.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.38/1.44
% 4.38/1.44 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.38/1.44
% 4.38/1.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.38/1.44 % ------ Proving...
% 4.38/1.44 % ------ Problem Properties
% 4.38/1.44
% 4.38/1.44 %
% 4.38/1.44 % clauses 48
% 4.38/1.44 % conjectures 6
% 4.38/1.44 % EPR 21
% 4.38/1.44 % Horn 44
% 4.38/1.44 % unary 24
% 4.38/1.44 % binary 13
% 4.38/1.44 % lits 94
% 4.38/1.44 % lits eq 0
% 4.38/1.44 % fd_pure 0
% 4.38/1.44 % fd_pseudo 0
% 4.38/1.44 % fd_cond 0
% 4.38/1.44 % fd_pseudo_cond 0
% 4.38/1.44 % AC symbols 0
% 4.38/1.44
% 4.38/1.44 % ------ Schedule dynamic 5 is on
% 4.38/1.44
% 4.38/1.44 % ------ no equalities: superposition off
% 4.38/1.44
% 4.38/1.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.38/1.44
% 4.38/1.44
% 4.38/1.44 % ------
% 4.38/1.44 % Current options:
% 4.38/1.44 % ------
% 4.38/1.44
% 4.38/1.44
% 4.38/1.44 %
% 4.38/1.44
% 4.38/1.44 % ------ Proving...
% 4.38/1.44 %
% 4.38/1.44
% 4.38/1.44 % SZS status Theorem for theBenchmark.p
% 4.38/1.44
% 4.38/1.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.38/1.45
% 4.38/1.45
%------------------------------------------------------------------------------