%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN076+1 : 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 : n012.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 6.75s 1.51s
% Output : CNFRefutation 6.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 23 unt; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 205 ( 92 ~; 77 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-1 aty)
% Number of variables : 145 ( 0 sgn 119 !; 26 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( r1(X3)
& id(X1,X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(f17,axiom,
! [X0] :
( ? [X2,X3] :
( r2(X2,X3)
& id(X0,X3) )
| ? [X1] :
( r1(X1)
& id(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6a) ).
fof(f19,conjecture,
? [X0,X1,X2] :
( ? [X7] :
( r3(X1,X2,X7)
& id(X7,X0) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& id(X3,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thereexistsanevennumberid) ).
fof(f20,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X7] :
( r3(X1,X2,X7)
& id(X7,X0) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& id(X3,X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ! [X7] :
( ~ r3(X1,X2,X7)
| ~ id(X7,X0) )
| ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) )
| ~ r2(X5,X4) )
| ~ r4(X4,X1,X3) )
| ~ id(X3,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X1] :
( ( ~ id(X1,sK0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f23,plain,
! [X0,X2] :
( ( ~ id(X2,sK1(X0))
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f28,plain,
! [X0] :
( r3(X0,sK13(X0),sK12(X0))
& r1(sK13(X0))
& id(sK12(X0),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f15]) ).
fof(f29,plain,
! [X0] :
( r1(sK16(X0))
& id(sK14(X0),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))],[f16]) ).
fof(f30,plain,
! [X0] :
( ( r2(sK18(X0),sK19(X0))
& id(X0,sK19(X0)) )
| ( r1(sK17(X0))
& id(X0,sK17(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X1,sK17(X0)),skolemize(X2,sK18(X0)),skolemize(X3,sK19(X0))],[f17]) ).
fof(f34,plain,
! [X1] :
( ~ r1(X1)
| id(X1,sK0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0] :
( ~ id(X2,sK1(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f77,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f78,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f79,plain,
! [X0] : id(sK12(X0),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f80,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f81,plain,
! [X0] : id(sK14(X0),sK16(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f82,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f83,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f85,plain,
! [X0] :
( id(X0,sK19(X0))
| r1(sK17(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r3(X1,X2,X7)
| ~ id(X7,X0)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X3)
| ~ id(X3,X0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i] :
( id(X0,sK0)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( r2(X1,X0)
| ~ id(X0,sK1(X1)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_57,plain,
! [X0: $i] : id(X0,X0),
inference(cnf_transformation,[],[f47]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_79,plain,
! [X0: $i] : id(sK12(X0),X0),
inference(cnf_transformation,[],[f79]) ).
tcf(c_80,plain,
! [X0: $i] : r1(sK13(X0)),
inference(cnf_transformation,[],[f78]) ).
tcf(c_81,plain,
! [X0: $i] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f77]) ).
tcf(c_82,plain,
! [X0: $i] : r1(sK15(X0)),
inference(cnf_transformation,[],[f83]) ).
tcf(c_83,plain,
! [X0: $i] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f82]) ).
tcf(c_84,plain,
! [X0: $i] : id(sK14(X0),sK16(X0)),
inference(cnf_transformation,[],[f81]) ).
tcf(c_85,plain,
! [X0: $i] : r1(sK16(X0)),
inference(cnf_transformation,[],[f80]) ).
tcf(c_88,plain,
! [X0: $i] :
( r1(sK17(X0))
| id(X0,sK19(X0)) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X6,X3)
| ~ id(X4,X5)
| ~ id(X2,X5)
| ~ r4(X3,X0,X4)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_428,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X6,X3)
| ~ id(X4,X5)
| ~ id(X2,X5)
| ~ r4(X3,X0,X4)
| ~ r3(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X4,X0)
| ~ id(X2,X3)
| ~ id(sK12(X1),X3)
| ~ r4(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_81,c_428]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ id(sK14(X0),X1)
| ~ id(sK12(sK15(X0)),X1) ),
inference(superposition,[status(thm)],[c_83,c_897]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X1)
| ~ r2(X1,X0)
| ~ r1(sK12(sK15(X0)))
| ~ id(sK14(X0),sK0) ),
inference(superposition,[status(thm)],[c_49,c_925]) ).
tcf(c_1404,plain,
! [X0: $i] : id(X0,sK12(X0)),
inference(superposition,[status(thm)],[c_79,c_58]) ).
tcf(c_1405,plain,
! [X0: $i] : id(sK16(X0),sK14(X0)),
inference(superposition,[status(thm)],[c_84,c_58]) ).
tcf(c_1602,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(sK17(sK12(sK15(X0))))
| ~ r1(X2)
| ~ r2(X2,X1)
| ~ r2(X1,X0)
| ~ id(sK14(X0),sK19(sK12(sK15(X0)))) ),
inference(superposition,[status(thm)],[c_88,c_925]) ).
tcf(c_2102,plain,
! [X0: $i] :
( id(sK14(X0),sK0)
| ~ r1(sK14(X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2135,plain,
! [X0: $i] : r2(X0,sK1(X0)),
inference(superposition,[status(thm)],[c_57,c_52]) ).
tcf(c_3267,plain,
! [X0: $i] :
( r1(sK12(X0))
| ~ r1(X0) ),
inference(superposition,[status(thm)],[c_1404,c_60]) ).
tcf(c_3268,plain,
! [X0: $i] :
( r1(sK14(X0))
| ~ r1(sK16(X0)) ),
inference(superposition,[status(thm)],[c_1405,c_60]) ).
tcf(c_3275,plain,
! [X0: $i] : r1(sK14(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_3268,c_85]) ).
tcf(c_3460,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(sK15(X0))
| ~ r2(X2,X1)
| ~ r2(X1,X0)
| ~ id(sK14(X0),sK0) ),
inference(superposition,[status(thm)],[c_3267,c_1145]) ).
tcf(c_3462,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X1)
| ~ r2(X1,X0)
| ~ id(sK14(X0),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3460,c_82]) ).
tcf(c_10212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r2(X1,X0)
| ~ r2(X2,X1)
| ~ r1(X2) ),
inference(global_subsumption_just,[status(thm)],[c_1602,c_2102,c_3275,c_3462]) ).
tcf(c_10213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(renaming,[status(thm)],[c_10212]) ).
tcf(c_10225,plain,
! [X0: $i,X1: $i] :
( ~ r1(X0)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_2135,c_10213]) ).
tcf(c_10771,plain,
! [X0: $i] : ~ r1(X0),
inference(superposition,[status(thm)],[c_2135,c_10225]) ).
tcf(c_10773,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_80,c_10771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Thu Sep 24 05:57:22 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.06/0.33 Running first-order theorem proving
% 0.06/0.33 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
% 0.06/0.33
% 0.06/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.06/0.33
% 0.06/0.33 % Detected problem language: tptp
% 0.06/0.34 % Proving...
% 6.75/1.51 % SZS status Started for theBenchmark.p
% 6.75/1.51 % SZS status Theorem for theBenchmark.p
% 6.75/1.51
% 6.75/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.75/1.51
% 6.75/1.51 % ------ iProver source info
% 6.75/1.51
% 6.75/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 6.75/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.75/1.51 % git: non_committed_changes: false
% 6.75/1.51
% 6.75/1.51 % ------ Parsing...
% 6.75/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.75/1.51
% 6.75/1.51 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.75/1.51
% 6.75/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.75/1.51 % ------ Proving...
% 6.75/1.51 % ------ Problem Properties
% 6.75/1.51
% 6.75/1.51 %
% 6.75/1.51 % clauses 43
% 6.75/1.51 % conjectures 1
% 6.75/1.51 % EPR 16
% 6.75/1.51 % Horn 39
% 6.75/1.51 % unary 18
% 6.75/1.51 % binary 13
% 6.75/1.51 % lits 95
% 6.75/1.51 % lits eq 0
% 6.75/1.51 % fd_pure 0
% 6.75/1.51 % fd_pseudo 0
% 6.75/1.51 % fd_cond 0
% 6.75/1.51 % fd_pseudo_cond 0
% 6.75/1.51 % AC symbols 0
% 6.75/1.51
% 6.75/1.51 % ------ Schedule dynamic 5 is on
% 6.75/1.51
% 6.75/1.51 % ------ no equalities: superposition off
% 6.75/1.51
% 6.75/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.75/1.51
% 6.75/1.51
% 6.75/1.51 % ------
% 6.75/1.51 % Current options:
% 6.75/1.51 % ------
% 6.75/1.51
% 6.75/1.51
% 6.75/1.51 %
% 6.75/1.51
% 6.75/1.51 % ------ Proving...
% 6.75/1.51 %
% 6.75/1.51
% 6.75/1.51 % SZS status Theorem for theBenchmark.p
% 6.75/1.51
% 6.75/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.75/1.51
% 6.75/1.51
%------------------------------------------------------------------------------