%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN076+2 : 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 : n018.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 02:29:58 PM UTC 2026
% Result : Theorem 0.94s 1.19s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 23 unt; 0 def)
% Number of atoms : 119 ( 30 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 58 ~; 43 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 108 ( 0 sgn 85 !; 23 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X1 = X0
& r1(X1) )
| ( X1 != X0
& ~ r1(X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( X1 = X0
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( X1 = X3
& r1(X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( ? [X7] :
( X7 = X0
& r3(X1,X2,X7) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& X3 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thereexistsanevennumber) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X7] :
( X7 = X0
& r3(X1,X2,X7) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& X3 = X0 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ! [X7] :
( X0 != X7
| ~ r3(X1,X2,X7) )
| ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) )
| ~ r2(X5,X4) )
| ~ r4(X4,X1,X3) )
| X0 != X3 ) ),
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(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(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(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,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X7
| ~ r3(X1,X2,X7)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X3)
| X0 != X3 ),
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(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( X3 != X7
| ~ r3(X1,X2,X7)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X3) ),
inference(equality_resolution,[],[f63]) ).
fof(f78,plain,
! [X2,X1,X6,X7,X4,X5] :
( ~ r3(X1,X2,X7)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X7) ),
inference(equality_resolution,[],[f77]) ).
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_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_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,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r4(X3,X0,X2)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_193,plain,
! [X0: $i] : r3(X0,sK13(X0),X0),
inference(light_normalisation,[status(thm)],[c_67,c_68]) ).
tcf(c_676,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r4(X3,X0,X2)
| ~ r3(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r4(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_193,c_676]) ).
tcf(c_970,plain,
! [X0: $i] : sK15(X0) = sK0,
inference(superposition,[status(thm)],[c_69,c_49]) ).
tcf(c_971,plain,
! [X0: $i] : sK16(X0) = sK0,
inference(superposition,[status(thm)],[c_71,c_49]) ).
tcf(c_974,plain,
! [X0: $i] : r4(X0,sK0,sK16(X0)),
inference(demodulation,[status(thm)],[c_70,c_970]) ).
tcf(c_1004,plain,
! [X0: $i] : r4(X0,sK0,sK0),
inference(light_normalisation,[status(thm)],[c_974,c_971]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_1004,c_949]) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i] :
( ~ r1(X0)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_1005]) ).
tcf(c_1026,plain,
! [X0: $i] : ~ r1(X0),
inference(superposition,[status(thm)],[c_52,c_1015]) ).
tcf(c_1029,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_1026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 05:59:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.94/1.19 % SZS status Started for theBenchmark.p
% 0.94/1.19 % SZS status Theorem for theBenchmark.p
% 0.94/1.19
% 0.94/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.19
% 0.94/1.19 % ------ iProver source info
% 0.94/1.19
% 0.94/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.19 % git: non_committed_changes: false
% 0.94/1.19
% 0.94/1.19 % ------ Parsing...
% 0.94/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.94/1.19
% 0.94/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.94/1.19
% 0.94/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.94/1.19
% 0.94/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.94/1.19 % ------ Proving...
% 0.94/1.19 % ------ Problem Properties
% 0.94/1.19
% 0.94/1.19 %
% 0.94/1.19 % clauses 29
% 0.94/1.19 % conjectures 1
% 0.94/1.19 % EPR 5
% 0.94/1.19 % Horn 25
% 0.94/1.19 % unary 18
% 0.94/1.19 % binary 9
% 0.94/1.19 % lits 44
% 0.94/1.19 % lits eq 10
% 0.94/1.19 % fd_pure 0
% 0.94/1.19 % fd_pseudo 0
% 0.94/1.19 % fd_cond 1
% 0.94/1.19 % fd_pseudo_cond 4
% 0.94/1.19 % AC symbols 0
% 0.94/1.19
% 0.94/1.19 % ------ Schedule dynamic 5 is on
% 0.94/1.19
% 0.94/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.94/1.19
% 0.94/1.19
% 0.94/1.19 % ------
% 0.94/1.19 % Current options:
% 0.94/1.19 % ------
% 0.94/1.19
% 0.94/1.19
% 0.94/1.19 %
% 0.94/1.19
% 0.94/1.19 % ------ Proving...
% 0.94/1.19 %
% 0.94/1.19
% 0.94/1.19 % SZS status Theorem for theBenchmark.p
% 0.94/1.19
% 0.94/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.19
% 0.94/1.19
%------------------------------------------------------------------------------