%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN085+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 : n001.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 3.37s 1.28s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 91 ( 63 unt; 1 def)
% Number of atoms : 183 ( 70 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 55 ~; 40 |; 34 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 112 !; 14 ?; 55 :)
% 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(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r3(X0,X1,X3) )
| ( X3 != X2
& ~ r3(X0,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( X3 = X2
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
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(f11,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X2 != X1
| ~ r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(f12,conjecture,
! [X0] :
( ! [X4] :
( ~ r1(X4)
| X0 != X4 )
| ! [X1] :
( ! [X3] :
( ~ r2(X3,X1)
| ~ r1(X3) )
| ! [X2] :
( ~ r3(X2,X1,X0)
| ~ r1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplusoneidzero) ).
fof(f13,negated_conjecture,
~ ! [X0] :
( ! [X4] :
( ~ r1(X4)
| X0 != X4 )
| ! [X1] :
( ! [X3] :
( ~ r2(X3,X1)
| ~ r1(X3) )
| ! [X2] :
( ~ r3(X2,X1,X0)
| ~ r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
( ? [X4] :
( r1(X4)
& X0 = X4 )
& ? [X1] :
( ? [X3] :
( r2(X3,X1)
& r1(X3) )
& ? [X2] :
( r3(X2,X1,X0)
& r1(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(f17,plain,
! [X0,X1,X3] :
( ( sK2(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK2(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( r3(X0,X1,sK7(X0,X1))
& r2(sK7(X0,X1),sK4(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& r2(X1,sK6(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
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(f24,plain,
( r1(sK24)
& sK20 = sK24
& r2(sK23,sK21)
& r1(sK23)
& r3(sK22,sK21,sK20)
& r1(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24)],[f14]) ).
fof(f27,plain,
! [X1] :
( sK0 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0] :
( sK1(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X3,X0,X1] :
( sK2(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f52,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
r1(sK24),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
sK20 = sK24,
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
r2(sK23,sK21),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
r1(sK23),
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
r3(sK22,sK21,sK20),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
r1(sK22),
inference(cnf_transformation,[],[f24]) ).
fof(f70,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f42,f43]) ).
fof(f73,plain,
r3(sK22,sK21,sK24),
inference(definition_unfolding,[],[f68,f65]) ).
fof(f83,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ r1(X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( sK1(X0) = X1 )
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(X0,X1) = X2 )
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : r2(X0,sK6(X1,X0)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f70]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,plain,
! [X0: $i] : r1(sK13(X0)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_67,plain,
! [X0: $i] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_68,plain,
! [X0: $i] : sK12(X0) = X0,
inference(cnf_transformation,[],[f52]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_77,negated_conjecture,
r1(sK22),
inference(cnf_transformation,[],[f69]) ).
tcf(c_78,negated_conjecture,
r3(sK22,sK21,sK24),
inference(cnf_transformation,[],[f73]) ).
tcf(c_79,negated_conjecture,
r1(sK23),
inference(cnf_transformation,[],[f67]) ).
tcf(c_80,negated_conjecture,
r2(sK23,sK21),
inference(cnf_transformation,[],[f66]) ).
tcf(c_81,negated_conjecture,
r1(sK24),
inference(cnf_transformation,[],[f64]) ).
tcf(c_197,plain,
! [X0: $i] : r3(X0,sK13(X0),X0),
inference(light_normalisation,[status(thm)],[c_67,c_68]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK2(X0,X3) = X4 )
| ( X0 != X1 )
| ( sK5(X1,X2) != X4 )
| ( sK6(X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_58]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] : sK2(X0,sK6(X0,X1)) = sK5(X0,X1),
inference(unflattening,[status(thm)],[c_271]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK2(X0,X2) = X4 )
| ( X2 != X3 )
| ( X0 != X1 )
| ( sK7(X1,X3) != X4 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_60]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] : sK2(X0,X1) = sK7(X0,X1),
inference(unflattening,[status(thm)],[c_277]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(X0,X1) = X2 )
| ( X2 != sK24 )
| ( X1 != sK21 )
| ( X0 != sK22 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_78]) ).
tcf(c_290,plain,
sK2(sK22,sK21) = sK24,
inference(unflattening,[status(thm)],[c_289]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK2(X0,X2) = X3 )
| ( X1 != X3 )
| ( X0 != X1 )
| ( sK13(X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_197]) ).
tcf(c_295,plain,
! [X0: $i] : sK2(X0,sK13(X0)) = X0,
inference(unflattening,[status(thm)],[c_294]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i] : r2(sK2(X0,X1),sK5(X0,X1)),
inference(demodulation,[status(thm)],[c_59,c_278]) ).
tcf(c_676,definition,
iPr_def_10 = sK2(sK22,sK21),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_677,plain,
iPr_def_10 = sK24,
inference(demodulation,[status(thm)],[c_290,c_676]) ).
tcf(c_678,negated_conjecture,
r1(sK24),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_679,negated_conjecture,
r2(sK23,sK21),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_680,negated_conjecture,
r1(sK23),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_681,negated_conjecture,
r1(sK22),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_915,plain,
r1(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_678,c_677]) ).
tcf(c_920,plain,
! [X0: $i] : sK13(X0) = sK0,
inference(superposition,[status(thm)],[c_66,c_49]) ).
tcf(c_923,plain,
sK0 = sK22,
inference(superposition,[status(thm)],[c_681,c_49]) ).
tcf(c_924,plain,
sK0 = sK23,
inference(superposition,[status(thm)],[c_680,c_49]) ).
tcf(c_925,plain,
sK0 = iPr_def_10,
inference(superposition,[status(thm)],[c_915,c_49]) ).
tcf(c_930,plain,
sK2(sK0,sK21) = iPr_def_10,
inference(demodulation,[status(thm)],[c_676,c_923]) ).
tcf(c_932,plain,
r2(sK0,sK21),
inference(demodulation,[status(thm)],[c_679,c_924]) ).
tcf(c_938,plain,
r2(iPr_def_10,sK21),
inference(light_normalisation,[status(thm)],[c_932,c_925]) ).
tcf(c_942,plain,
sK2(iPr_def_10,sK21) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_930,c_925]) ).
tcf(c_947,plain,
! [X0: $i] : sK13(X0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_920,c_925]) ).
tcf(c_960,plain,
~ r1(sK21),
inference(superposition,[status(thm)],[c_938,c_76]) ).
tcf(c_992,plain,
! [X0: $i,X1: $i] : sK6(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_57,c_51]) ).
tcf(c_996,plain,
sK1(iPr_def_10) = sK21,
inference(superposition,[status(thm)],[c_938,c_51]) ).
tcf(c_1114,plain,
! [X0: $i] : sK2(X0,iPr_def_10) = X0,
inference(light_normalisation,[status(thm)],[c_295,c_947]) ).
tcf(c_1115,plain,
! [X0: $i] : r2(X0,sK5(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_1114,c_519]) ).
tcf(c_1118,plain,
! [X0: $i] : sK5(X0,iPr_def_10) = sK1(X0),
inference(superposition,[status(thm)],[c_1115,c_51]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i] : sK2(X0,sK1(X1)) = sK5(X0,X1),
inference(light_normalisation,[status(thm)],[c_272,c_992]) ).
tcf(c_1440,plain,
! [X0: $i] : sK2(X0,sK21) = sK5(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_996,c_1437]) ).
tcf(c_1443,plain,
! [X0: $i] : sK2(X0,sK21) = sK1(X0),
inference(light_normalisation,[status(thm)],[c_1440,c_1118]) ).
tcf(c_1446,plain,
sK1(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_942,c_1443]) ).
tcf(c_1447,plain,
sK21 = iPr_def_10,
inference(demodulation,[status(thm)],[c_996,c_1446]) ).
tcf(c_1458,plain,
~ r1(iPr_def_10),
inference(demodulation,[status(thm)],[c_960,c_1447]) ).
tcf(c_1460,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1458,c_915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN085+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 06:05:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.37/1.28 % SZS status Started for theBenchmark.p
% 3.37/1.28 % SZS status Theorem for theBenchmark.p
% 3.37/1.28
% 3.37/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.37/1.28
% 3.37/1.28 % ------ iProver source info
% 3.37/1.28
% 3.37/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.37/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.37/1.28 % git: non_committed_changes: false
% 3.37/1.28
% 3.37/1.28 % ------ Parsing...
% 3.37/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.37/1.28
% 3.37/1.28 % ------ 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 %
% 3.37/1.28
% 3.37/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.37/1.28
% 3.37/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.37/1.28 % ------ Proving...
% 3.37/1.28 % ------ Problem Properties
% 3.37/1.28
% 3.37/1.28 %
% 3.37/1.28 % clauses 30
% 3.37/1.28 % conjectures 4
% 3.37/1.28 % EPR 9
% 3.37/1.28 % Horn 26
% 3.37/1.28 % unary 22
% 3.37/1.28 % binary 7
% 3.37/1.28 % lits 39
% 3.37/1.28 % lits eq 17
% 3.37/1.28 % fd_pure 0
% 3.37/1.28 % fd_pseudo 0
% 3.37/1.28 % fd_cond 1
% 3.37/1.28 % fd_pseudo_cond 2
% 3.37/1.28 % AC symbols 0
% 3.37/1.28
% 3.37/1.28 % ------ Schedule dynamic 5 is on
% 3.37/1.28
% 3.37/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.37/1.28
% 3.37/1.28
% 3.37/1.28 % ------
% 3.37/1.28 % Current options:
% 3.37/1.28 % ------
% 3.37/1.28
% 3.37/1.28
% 3.37/1.28 %
% 3.37/1.28
% 3.37/1.28 % ------ Proving...
% 3.37/1.28 %
% 3.37/1.28
% 3.37/1.28 % SZS status Theorem for theBenchmark.p
% 3.37/1.28
% 3.37/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.37/1.28
% 3.37/1.28
%------------------------------------------------------------------------------