%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN073+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 : n026.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 02:29:57 PM UTC 2026
% Result : Theorem 1.53s 6.41s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 31 unt; 0 def)
% Number of atoms : 107 ( 33 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 49 ~; 36 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 55 ( 0 sgn 48 !; 7 ?; 9 :)
% 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(f7,axiom,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X3 != X2
| ~ r2(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
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] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( X1 != X0
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneuneqtwo) ).
fof(f13,negated_conjecture,
~ ! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( X1 != X0
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
( ? [X3] :
( r2(X3,X0)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) )
& ? [X1] :
( X0 = X1
& ? [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(f24,plain,
( r2(sK23,sK20)
& r2(sK24,sK23)
& r1(sK24)
& sK20 = sK21
& r2(sK22,sK21)
& 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(f26,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f15]) ).
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(f51,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
r2(sK23,sK20),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
r2(sK24,sK23),
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
r1(sK24),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
sK20 = sK21,
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
r2(sK22,sK21),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
r1(sK22),
inference(cnf_transformation,[],[f24]) ).
fof(f73,plain,
r2(sK23,sK21),
inference(definition_unfolding,[],[f64,f67]) ).
fof(f74,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f82,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f51]) ).
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_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f74]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( sK1(X0) = X1 )
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
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,
r2(sK22,sK21),
inference(cnf_transformation,[],[f68]) ).
tcf(c_79,negated_conjecture,
r1(sK24),
inference(cnf_transformation,[],[f66]) ).
tcf(c_80,negated_conjecture,
r2(sK24,sK23),
inference(cnf_transformation,[],[f65]) ).
tcf(c_81,negated_conjecture,
r2(sK23,sK21),
inference(cnf_transformation,[],[f73]) ).
tcf(c_645,negated_conjecture,
r2(sK23,sK21),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_646,negated_conjecture,
r2(sK24,sK23),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_647,negated_conjecture,
r1(sK24),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_648,negated_conjecture,
r2(sK22,sK21),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_649,negated_conjecture,
r1(sK22),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_885,plain,
sK0 = sK22,
inference(superposition,[status(thm)],[c_649,c_49]) ).
tcf(c_886,plain,
sK0 = sK24,
inference(superposition,[status(thm)],[c_647,c_49]) ).
tcf(c_890,plain,
r2(sK0,sK21),
inference(demodulation,[status(thm)],[c_648,c_885]) ).
tcf(c_892,plain,
r2(sK0,sK23),
inference(demodulation,[status(thm)],[c_646,c_886]) ).
tcf(c_903,plain,
~ r1(sK21),
inference(superposition,[status(thm)],[c_890,c_76]) ).
tcf(c_934,plain,
sK1(sK0) = sK21,
inference(superposition,[status(thm)],[c_890,c_51]) ).
tcf(c_935,plain,
sK1(sK0) = sK23,
inference(superposition,[status(thm)],[c_892,c_51]) ).
tcf(c_962,plain,
sK21 = sK23,
inference(light_normalisation,[status(thm)],[c_935,c_934]) ).
tcf(c_966,plain,
r2(sK21,sK21),
inference(demodulation,[status(thm)],[c_645,c_962]) ).
tcf(c_1006,plain,
! [X0: $i] :
( ( X0 = sK0 )
| ~ r2(X0,sK21) ),
inference(superposition,[status(thm)],[c_890,c_65]) ).
tcf(c_1035,plain,
sK0 = sK21,
inference(superposition,[status(thm)],[c_966,c_1006]) ).
tcf(c_1041,plain,
~ r1(sK0),
inference(demodulation,[status(thm)],[c_903,c_1035]) ).
tcf(c_1043,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1041,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN073+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.45 % Computer : n026.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Thu Sep 24 05:58:30 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.22/5.50 Running first-order theorem proving
% 0.22/5.50 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
% 0.22/5.52
% 0.22/5.52 % ======== iProver multi-core TPTP/SMT =========
% 0.22/5.52
% 0.22/5.52 % Detected problem language: tptp
% 0.22/5.53 % Proving...
% 1.53/6.41 % SZS status Started for theBenchmark.p
% 1.53/6.41 % SZS status Theorem for theBenchmark.p
% 1.53/6.41
% 1.53/6.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.53/6.41
% 1.53/6.41 % ------ iProver source info
% 1.53/6.41
% 1.53/6.41 % git: date: 2026-07-19 20:42:38 +0200
% 1.53/6.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.53/6.41 % git: non_committed_changes: false
% 1.53/6.41
% 1.53/6.41 % ------ Parsing...
% 1.53/6.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.53/6.41
% 1.53/6.41 % ------ 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 %
% 1.53/6.41
% 1.53/6.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.53/6.41
% 1.53/6.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.53/6.41 % ------ Proving...
% 1.53/6.41 % ------ Problem Properties
% 1.53/6.41
% 1.53/6.41 %
% 1.53/6.41 % clauses 29
% 1.53/6.41 % conjectures 5
% 1.53/6.41 % EPR 9
% 1.53/6.41 % Horn 25
% 1.53/6.41 % unary 21
% 1.53/6.41 % binary 7
% 1.53/6.41 % lits 38
% 1.53/6.41 % lits eq 15
% 1.53/6.41 % fd_pure 0
% 1.53/6.41 % fd_pseudo 0
% 1.53/6.41 % fd_cond 1
% 1.53/6.41 % fd_pseudo_cond 2
% 1.53/6.41 % AC symbols 0
% 1.53/6.41
% 1.53/6.41 % ------ Schedule dynamic 5 is on
% 1.53/6.41
% 1.53/6.41 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.53/6.41
% 1.53/6.41
% 1.53/6.41 % ------
% 1.53/6.41 % Current options:
% 1.53/6.41 % ------
% 1.53/6.41
% 1.53/6.41
% 1.53/6.41 %
% 1.53/6.41
% 1.53/6.41 % ------ Proving...
% 1.53/6.41 %
% 1.53/6.41
% 1.53/6.41 % SZS status Theorem for theBenchmark.p
% 1.53/6.41
% 1.53/6.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.53/6.41
% 1.53/6.41
%------------------------------------------------------------------------------