%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN055+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 : n015.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 3.52s 1.17s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 33 unt; 0 def)
% Number of atoms : 180 ( 36 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 210 ( 94 ~; 76 |; 40 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 136 !; 25 ?; 70 :)
% 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(f12,conjecture,
? [X0] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& X0 = X5 )
& ? [X1] :
( ? [X4] :
( r3(X4,X1,X0)
& r1(X4) )
& ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r2(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplustwoeqtwo) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& X0 = X5 )
& ? [X1] :
( ? [X4] :
( r3(X4,X1,X0)
& r1(X4) )
& ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r2(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ r2(X7,X6)
| ~ r1(X7) )
| ~ r2(X6,X5) )
| X0 != X5 )
| ! [X1] :
( ! [X4] :
( ~ r3(X4,X1,X0)
| ~ r1(X4) )
| ! [X2] :
( ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) )
| ~ r2(X2,X1) ) ) ),
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(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(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
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(f63,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| X0 != X5
| ~ r3(X4,X1,X0)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f41,f42]) ).
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] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r3(X4,X1,X5)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X1) ),
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_57,plain,
! [X0: $i,X1: $i] : r2(X0,sK6(X1,X0)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f40]) ).
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_77,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ r1(X6)
| ~ r1(X4)
| ~ r1(X0)
| ~ r2(X6,X5)
| ~ r2(X5,X2)
| ~ r2(X4,X3)
| ~ r2(X3,X1)
| ~ r3(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_81,plain,
r2(sK0,sK1(sK0)),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_199,plain,
! [X0: $i] : r3(X0,sK13(X0),X0),
inference(light_normalisation,[status(thm)],[c_67,c_68]) ).
tcf(c_738,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ r1(X6)
| ~ r1(X4)
| ~ r1(X0)
| ~ r2(X6,X5)
| ~ r2(X5,X2)
| ~ r2(X4,X3)
| ~ r2(X3,X1)
| ~ r3(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_1036,plain,
! [X0: $i] : sK13(X0) = sK0,
inference(superposition,[status(thm)],[c_66,c_49]) ).
tcf(c_1039,plain,
! [X0: $i] : r3(X0,sK0,X0),
inference(demodulation,[status(thm)],[c_199,c_1036]) ).
tcf(c_1186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ r1(X5)
| ~ r1(X4)
| ~ r1(X1)
| ~ r2(X5,X3)
| ~ r2(X4,X0)
| ~ r2(X3,sK5(X1,X2))
| ~ r2(X0,sK6(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_738]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ r1(X4)
| ~ r1(X3)
| ~ r1(X1)
| ~ r2(X4,X0)
| ~ r2(X3,X2)
| ~ r2(X0,sK5(X1,X2)) ),
inference(superposition,[status(thm)],[c_57,c_1186]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X1)
| ~ r1(X0)
| ~ r2(X3,X2)
| ~ r2(X0,sK7(X1,X2)) ),
inference(superposition,[status(thm)],[c_59,c_1223]) ).
tcf(c_1300,plain,
! [X0: $i,X1: $i] : sK6(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_57,c_51]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] : r3(X0,sK1(X1),sK5(X0,X1)),
inference(demodulation,[status(thm)],[c_58,c_1300]) ).
tcf(c_1356,plain,
! [X0: $i,X1: $i] : sK2(X0,X1) = sK7(X0,X1),
inference(superposition,[status(thm)],[c_60,c_53]) ).
tcf(c_1358,plain,
! [X0: $i] : sK2(X0,sK0) = X0,
inference(superposition,[status(thm)],[c_1039,c_53]) ).
tcf(c_1360,plain,
! [X0: $i,X1: $i] : r2(sK2(X0,X1),sK5(X0,X1)),
inference(demodulation,[status(thm)],[c_59,c_1356]) ).
tcf(c_1362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X1)
| ~ r1(X0)
| ~ r2(X3,X2)
| ~ r2(X0,sK2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_1242,c_1356]) ).
tcf(c_1382,plain,
! [X0: $i,X1: $i] : sK2(X0,sK1(X1)) = sK5(X0,X1),
inference(superposition,[status(thm)],[c_1307,c_53]) ).
tcf(c_1507,plain,
! [X0: $i] : r2(X0,sK5(X0,sK0)),
inference(superposition,[status(thm)],[c_1358,c_1360]) ).
tcf(c_1524,plain,
r2(sK0,sK5(sK0,sK0)),
inference(instantiation,[status(thm)],[c_1507]) ).
tcf(c_1802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ r1(X3)
| ~ r1(X1)
| ~ r1(X0)
| ~ r2(X3,sK1(X2))
| ~ r2(X0,sK5(X1,X2)) ),
inference(superposition,[status(thm)],[c_1382,c_1362]) ).
tcf(c_1823,plain,
( ~ r1(sK0)
| ~ r2(sK0,sK1(sK0))
| ~ r2(sK0,sK5(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_1802]) ).
tcf(c_1824,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1823,c_1524,c_81,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN055+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n015.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 05:53:40 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.52/1.17 % SZS status Started for theBenchmark.p
% 3.52/1.17 % SZS status Theorem for theBenchmark.p
% 3.52/1.17
% 3.52/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.52/1.17
% 3.52/1.17 % ------ iProver source info
% 3.52/1.17
% 3.52/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.52/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.52/1.17 % git: non_committed_changes: false
% 3.52/1.17
% 3.52/1.17 % ------ Parsing...
% 3.52/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.52/1.17
% 3.52/1.17 % ------ 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 %
% 3.52/1.17
% 3.52/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.52/1.17
% 3.52/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.52/1.17 % ------ Proving...
% 3.52/1.17 % ------ Problem Properties
% 3.52/1.17
% 3.52/1.17 %
% 3.52/1.17 % clauses 27
% 3.52/1.17 % conjectures 1
% 3.52/1.17 % EPR 5
% 3.52/1.17 % Horn 23
% 3.52/1.17 % unary 17
% 3.52/1.17 % binary 8
% 3.52/1.17 % lits 44
% 3.52/1.17 % lits eq 12
% 3.52/1.17 % fd_pure 0
% 3.52/1.17 % fd_pseudo 0
% 3.52/1.17 % fd_cond 1
% 3.52/1.17 % fd_pseudo_cond 3
% 3.52/1.17 % AC symbols 0
% 3.52/1.17
% 3.52/1.17 % ------ Schedule dynamic 5 is on
% 3.52/1.17
% 3.52/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.52/1.17
% 3.52/1.17
% 3.52/1.17 % ------
% 3.52/1.17 % Current options:
% 3.52/1.17 % ------
% 3.52/1.17
% 3.52/1.17
% 3.52/1.17 %
% 3.52/1.17
% 3.52/1.17 % ------ Proving...
% 3.52/1.17 %
% 3.52/1.17
% 3.52/1.17 % SZS status Theorem for theBenchmark.p
% 3.52/1.17
% 3.52/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.52/1.17
% 3.52/1.17
%------------------------------------------------------------------------------