%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN057+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 : n016.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 02:29:53 PM UTC 2026
% Result : Theorem 3.69s 1.28s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 66 ( 36 unt; 0 def)
% Number of atoms : 182 ( 40 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 207 ( 91 ~; 74 |; 42 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 164 ( 0 sgn 137 !; 27 ?; 68 :)
% 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(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r3(X0,X1,X3) )
| ( X3 != X2
& ~ r3(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
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] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( r2(X8,X7)
& r1(X8) )
& r2(X7,X6) )
& r3(X6,X6,X0) )
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& r2(X4,X3) )
& r2(X3,X2) )
& r2(X2,X1) )
& X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',twoplustwoeqfour) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( r2(X8,X7)
& r1(X8) )
& r2(X7,X6) )
& r3(X6,X6,X0) )
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& r2(X4,X3) )
& r2(X3,X2) )
& r2(X2,X1) )
& X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ r2(X8,X7)
| ~ r1(X8) )
| ~ r2(X7,X6) )
| ~ r3(X6,X6,X0) )
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ r1(X5) )
| ~ r2(X4,X3) )
| ~ r2(X3,X2) )
| ~ r2(X2,X1) )
| X0 != X1 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0] :
( sK3(X0) = X0
& r3(X0,sK4(X0),sK3(X0))
& r1(sK4(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f8]) ).
fof(f17,plain,
! [X1] :
( ( sK5 = X1
& r1(X1) )
| ( sK5 != X1
& ~ r1(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( r3(X0,X1,sK9(X0,X1))
& r2(sK9(X0,X1),sK6(X0,X1))
& sK6(X0,X1) = sK7(X0,X1)
& r3(X0,sK8(X0,X1),sK7(X0,X1))
& r2(X1,sK8(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f5]) ).
fof(f19,plain,
! [X0,X2] :
( ( sK10(X0) = X2
& r2(X0,X2) )
| ( sK10(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f2]) ).
fof(f20,plain,
! [X0,X1,X3] :
( ( sK11(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK11(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f3]) ).
fof(f21,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r3(X6,X6,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] : sK3(X0) = X0,
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0] : r3(X0,sK4(X0),sK3(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0] : r1(sK4(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X1] :
( r1(X1)
| sK5 != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X1] :
( sK5 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X0,X1] : r3(X0,X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] : r2(sK9(X0,X1),sK6(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X0,X1] : sK6(X0,X1) = sK7(X0,X1),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1] : r3(X0,sK8(X0,X1),sK7(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X0,X1] : r2(X1,sK8(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f41,plain,
! [X2,X0] :
( r2(X0,X2)
| sK10(X0) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X2,X0] :
( sK10(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X3,X0,X1] :
( sK11(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : r2(sK9(X0,X1),sK7(X0,X1)),
inference(definition_unfolding,[],[f36,f37]) ).
fof(f49,plain,
! [X2,X3,X1,X8,X6,X7,X4,X5] :
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r3(X6,X6,X1)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1) ),
inference(equality_resolution,[],[f21]) ).
fof(f51,plain,
r1(sK5),
inference(equality_resolution,[],[f31]) ).
fof(f54,plain,
! [X0] : r2(X0,sK10(X0)),
inference(equality_resolution,[],[f41]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ r1(X7)
| ~ r1(X5)
| ~ r2(X7,X6)
| ~ r2(X6,X0)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r3(X0,X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_55,plain,
! [X0: $i] : r1(sK4(X0)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i] : r3(X0,sK4(X0),sK3(X0)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,plain,
! [X0: $i] : sK3(X0) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ r1(X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
r1(sK5),
inference(cnf_transformation,[],[f51]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : r2(X0,sK8(X1,X0)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : r3(X0,sK8(X0,X1),sK7(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : r2(sK9(X0,X1),sK7(X0,X1)),
inference(cnf_transformation,[],[f48]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : r3(X0,X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( sK10(X0) = X1 )
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_66,plain,
! [X0: $i] : r2(X0,sK10(X0)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK11(X0,X1) = X2 )
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_70,plain,
r2(sK5,sK10(sK5)),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_163,plain,
! [X0: $i] : r3(X0,sK4(X0),X0),
inference(light_normalisation,[status(thm)],[c_56,c_57]) ).
tcf(c_669,plain,
! [X0: $i] : sK4(X0) = sK5,
inference(superposition,[status(thm)],[c_55,c_58]) ).
tcf(c_671,plain,
! [X0: $i] : r3(X0,sK5,X0),
inference(demodulation,[status(thm)],[c_163,c_669]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i] : sK8(X0,X1) = sK10(X1),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i] : sK10(sK9(X0,X1)) = sK7(X0,X1),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i] : r3(X0,sK10(X1),sK7(X0,X1)),
inference(demodulation,[status(thm)],[c_62,c_833]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ r1(X6)
| ~ r1(X5)
| ~ r2(X6,X2)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X0)
| ~ r2(X2,sK10(X1))
| ~ r2(X0,sK7(sK10(X1),X1)) ),
inference(superposition,[status(thm)],[c_838,c_49]) ).
tcf(c_1051,plain,
! [X0: $i,X1: $i] : sK9(X0,X1) = sK11(X0,X1),
inference(superposition,[status(thm)],[c_64,c_67]) ).
tcf(c_1053,plain,
! [X0: $i] : sK11(X0,sK5) = X0,
inference(superposition,[status(thm)],[c_671,c_67]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i] : sK11(X0,sK10(X1)) = sK7(X0,X1),
inference(superposition,[status(thm)],[c_838,c_67]) ).
tcf(c_1095,plain,
! [X0: $i] : sK9(X0,sK5) = X0,
inference(demodulation,[status(thm)],[c_1053,c_1051]) ).
tcf(c_1096,plain,
! [X0: $i] : sK7(X0,sK5) = sK10(X0),
inference(superposition,[status(thm)],[c_1095,c_834]) ).
tcf(c_1448,plain,
! [X0: $i,X1: $i] : sK9(X0,sK10(X1)) = sK7(X0,X1),
inference(demodulation,[status(thm)],[c_1054,c_1051]) ).
tcf(c_1451,plain,
! [X0: $i,X1: $i] : r2(sK7(X0,X1),sK7(X0,sK10(X1))),
inference(superposition,[status(thm)],[c_1448,c_63]) ).
tcf(c_1501,plain,
! [X0: $i] : r2(sK10(X0),sK7(X0,sK10(sK5))),
inference(superposition,[status(thm)],[c_1096,c_1451]) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ r1(X4)
| ~ r1(X3)
| ~ r2(X4,X1)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X1,sK10(sK10(sK5)))
| ~ r2(X0,sK10(sK10(sK10(sK5)))) ),
inference(superposition,[status(thm)],[c_1501,c_867]) ).
tcf(c_1614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X2)
| ~ r2(X3,X0)
| ~ r2(X2,X1)
| ~ r2(X1,sK10(sK10(sK5)))
| ~ r2(X0,sK10(sK10(sK5))) ),
inference(superposition,[status(thm)],[c_66,c_1570]) ).
tcf(c_1782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(X1)
| ~ r2(X2,X0)
| ~ r2(X1,sK10(sK5))
| ~ r2(X0,sK10(sK10(sK5))) ),
inference(superposition,[status(thm)],[c_66,c_1614]) ).
tcf(c_6146,plain,
! [X0: $i,X1: $i] :
( ~ r1(X1)
| ~ r1(X0)
| ~ r2(X1,sK10(sK5))
| ~ r2(X0,sK10(sK5)) ),
inference(superposition,[status(thm)],[c_66,c_1782]) ).
tcf(c_6163,plain,
( ~ r1(sK5)
| ~ r2(sK5,sK10(sK5)) ),
inference(instantiation,[status(thm)],[c_6146]) ).
tcf(c_6164,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6163,c_70,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN057+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 05:55:12 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.69/1.28 % SZS status Started for theBenchmark.p
% 3.69/1.28 % SZS status Theorem for theBenchmark.p
% 3.69/1.28
% 3.69/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.69/1.28
% 3.69/1.28 % ------ iProver source info
% 3.69/1.28
% 3.69/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.69/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.69/1.28 % git: non_committed_changes: false
% 3.69/1.28
% 3.69/1.28 % ------ Parsing...
% 3.69/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.69/1.28
% 3.69/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.69/1.28
% 3.69/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.69/1.28
% 3.69/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/1.28 % ------ Proving...
% 3.69/1.28 % ------ Problem Properties
% 3.69/1.28
% 3.69/1.28 %
% 3.69/1.28 % clauses 20
% 3.69/1.28 % conjectures 1
% 3.69/1.28 % EPR 5
% 3.69/1.28 % Horn 16
% 3.69/1.28 % unary 10
% 3.69/1.28 % binary 8
% 3.69/1.28 % lits 38
% 3.69/1.28 % lits eq 9
% 3.69/1.28 % fd_pure 0
% 3.69/1.28 % fd_pseudo 0
% 3.69/1.28 % fd_cond 1
% 3.69/1.28 % fd_pseudo_cond 3
% 3.69/1.28 % AC symbols 0
% 3.69/1.28
% 3.69/1.28 % ------ Schedule dynamic 5 is on
% 3.69/1.28
% 3.69/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.28
% 3.69/1.28
% 3.69/1.28 % ------
% 3.69/1.28 % Current options:
% 3.69/1.28 % ------
% 3.69/1.28
% 3.69/1.28
% 3.69/1.28 %
% 3.69/1.28
% 3.69/1.28 % ------ Proving...
% 3.69/1.28 %
% 3.69/1.28
% 3.69/1.28 % SZS status Theorem for theBenchmark.p
% 3.69/1.28
% 3.69/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.29
% 3.69/1.29
%------------------------------------------------------------------------------