%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN086+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 : n005.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 3.40s 1.27s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 47 unt; 0 def)
% Number of atoms : 178 ( 59 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 164 ( 68 ~; 52 |; 44 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 138 !; 23 ?; 65 :)
% 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(f4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r4(X0,X1,X3) )
| ( X3 != X2
& ~ r4(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
fof(f6,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r4(X0,X1,X5)
& r3(X5,X0,X2) )
& ? [X3] :
( X3 = X2
& ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
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(f9,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( X1 = X3
& r1(X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(f12,conjecture,
? [X0] :
( ? [X4] :
( X0 = X4
& r1(X4) )
& ? [X1] :
( ? [X3] :
( r4(X3,X1,X0)
& r1(X3) )
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerotimesoneeqzero) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X4] :
( X0 = X4
& r1(X4) )
& ? [X1] :
( ? [X3] :
( r4(X3,X1,X0)
& r1(X3) )
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X4] :
( X0 != X4
| ~ r1(X4) )
| ! [X1] :
( ! [X3] :
( ~ r4(X3,X1,X0)
| ~ r1(X3) )
| ! [X2] :
( ~ r2(X2,X1)
| ~ 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(f18,plain,
! [X0,X1,X3] :
( ( sK3(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK3(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( r4(X0,X1,sK11(X0,X1))
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& sK8(X0,X1) = sK9(X0,X1)
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& r2(X1,sK10(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f6]) ).
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(f30,plain,
! [X2,X0] :
( sK1(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X3,X0,X1] :
( sK2(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X3,X0,X1] :
( sK3(X0,X1) = X3
| ~ r4(X0,X1,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK8(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0,X1] : sK8(X0,X1) = sK9(X0,X1),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : r4(X0,sK10(X0,X1),sK9(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
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(f53,plain,
! [X0] : r1(sK13(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,X4] :
( X0 != X4
| ~ r1(X4)
| ~ r4(X3,X1,X0)
| ~ r1(X3)
| ~ r2(X2,X1)
| ~ r1(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f65,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK9(X0,X1)),
inference(definition_unfolding,[],[f46,f47]) ).
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,X4] :
( ~ r1(X4)
| ~ r4(X3,X1,X4)
| ~ r1(X3)
| ~ r2(X2,X1)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
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_51,plain,
! [X0: $i,X1: $i] :
( ( sK1(X0) = X1 )
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_52,plain,
! [X0: $i] : r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f69]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(X0,X1) = X2 )
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK3(X0,X1) = X2 )
| ~ r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : r2(X0,sK10(X1,X0)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : r4(X0,sK10(X0,X1),sK9(X0,X1)),
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : r3(sK11(X0,X1),X0,sK9(X0,X1)),
inference(cnf_transformation,[],[f65]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : r4(X0,X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,plain,
! [X0: $i] : r1(sK13(X0)),
inference(cnf_transformation,[],[f53]) ).
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] :
( ~ r1(X3)
| ~ r1(X2)
| ~ r1(X0)
| ~ r2(X3,X1)
| ~ r4(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_81,plain,
r2(sK0,sK1(sK0)),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_193,plain,
! [X0: $i] : r3(X0,sK13(X0),X0),
inference(light_normalisation,[status(thm)],[c_67,c_68]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK2(X2,X3) = X4 )
| ( X0 != X3 )
| ( sK11(X0,X1) != X2 )
| ( sK9(X0,X1) != X4 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_63]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : sK2(sK11(X0,X1),X0) = sK9(X0,X1),
inference(unflattening,[status(thm)],[c_266]) ).
tcf(c_272,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_193]) ).
tcf(c_273,plain,
! [X0: $i] : sK2(X0,sK13(X0)) = X0,
inference(unflattening,[status(thm)],[c_272]) ).
tcf(c_606,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X2)
| ~ r1(X0)
| ~ r2(X3,X1)
| ~ r4(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_880,plain,
! [X0: $i] : sK13(X0) = sK0,
inference(superposition,[status(thm)],[c_66,c_49]) ).
tcf(c_881,plain,
! [X0: $i] : sK15(X0) = sK0,
inference(superposition,[status(thm)],[c_69,c_49]) ).
tcf(c_882,plain,
! [X0: $i] : sK16(X0) = sK0,
inference(superposition,[status(thm)],[c_71,c_49]) ).
tcf(c_884,plain,
! [X0: $i] : r4(X0,sK0,sK16(X0)),
inference(demodulation,[status(thm)],[c_70,c_881]) ).
tcf(c_917,plain,
! [X0: $i] : r4(X0,sK0,sK0),
inference(light_normalisation,[status(thm)],[c_884,c_882]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i] : sK10(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_61,c_51]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] : r4(X0,sK1(X1),sK9(X0,X1)),
inference(demodulation,[status(thm)],[c_62,c_957]) ).
tcf(c_972,plain,
! [X0: $i] : sK2(X0,sK0) = X0,
inference(light_normalisation,[status(thm)],[c_273,c_880]) ).
tcf(c_1050,plain,
! [X0: $i,X1: $i] : sK3(X0,X1) = sK11(X0,X1),
inference(superposition,[status(thm)],[c_64,c_55]) ).
tcf(c_1051,plain,
! [X0: $i] : sK3(X0,sK0) = sK0,
inference(superposition,[status(thm)],[c_917,c_55]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i] : sK2(sK3(X0,X1),X0) = sK9(X0,X1),
inference(light_normalisation,[status(thm)],[c_267,c_1050]) ).
tcf(c_1135,plain,
! [X0: $i] : sK2(sK0,X0) = sK9(X0,sK0),
inference(superposition,[status(thm)],[c_1051,c_1132]) ).
tcf(c_1147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0)
| ~ r2(X1,sK1(X1))
| ~ r4(X0,sK1(X1),X2) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_1148,plain,
( ~ r1(sK0)
| ~ r2(sK0,sK1(sK0))
| ~ r4(sK0,sK1(sK0),sK0) ),
inference(instantiation,[status(thm)],[c_1147]) ).
tcf(c_1230,plain,
! [X0: $i] : r4(X0,sK1(sK0),sK2(sK0,X0)),
inference(superposition,[status(thm)],[c_1135,c_964]) ).
tcf(c_1238,plain,
r4(sK0,sK1(sK0),sK0),
inference(superposition,[status(thm)],[c_972,c_1230]) ).
tcf(c_1242,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1238,c_1148,c_81,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN086+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 06:00:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 3.40/1.27 % SZS status Started for theBenchmark.p
% 3.40/1.27 % SZS status Theorem for theBenchmark.p
% 3.40/1.27
% 3.40/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.40/1.27
% 3.40/1.27 % ------ iProver source info
% 3.40/1.27
% 3.40/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.40/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.40/1.27 % git: non_committed_changes: false
% 3.40/1.27
% 3.40/1.27 % ------ Parsing...
% 3.40/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.40/1.27
% 3.40/1.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 1 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.40/1.27
% 3.40/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.40/1.27
% 3.40/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.40/1.27 % ------ Proving...
% 3.40/1.27 % ------ Problem Properties
% 3.40/1.27
% 3.40/1.27 %
% 3.40/1.27 % clauses 27
% 3.40/1.27 % conjectures 1
% 3.40/1.27 % EPR 5
% 3.40/1.27 % Horn 23
% 3.40/1.27 % unary 17
% 3.40/1.27 % binary 8
% 3.40/1.27 % lits 41
% 3.40/1.27 % lits eq 13
% 3.40/1.27 % fd_pure 0
% 3.40/1.27 % fd_pseudo 0
% 3.40/1.27 % fd_cond 1
% 3.40/1.27 % fd_pseudo_cond 3
% 3.40/1.27 % AC symbols 0
% 3.40/1.27
% 3.40/1.27 % ------ Schedule dynamic 5 is on
% 3.40/1.27
% 3.40/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.40/1.27
% 3.40/1.27
% 3.40/1.27 % ------
% 3.40/1.27 % Current options:
% 3.40/1.27 % ------
% 3.40/1.27
% 3.40/1.27
% 3.40/1.27 %
% 3.40/1.27
% 3.40/1.27 % ------ Proving...
% 3.40/1.27 %
% 3.40/1.27
% 3.40/1.27 % SZS status Theorem for theBenchmark.p
% 3.40/1.27
% 3.40/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.40/1.27
% 3.40/1.27
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