%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PHI010+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 02:30:29 PM UTC 2026
% Result : Theorem 0.45s 1.28s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 11 unt; 2 def)
% Number of atoms : 211 ( 45 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 255 ( 92 ~; 85 |; 65 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 92 !; 14 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( is_the(X0,X1)
=> ( object(X0)
& property(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_is_property_and_described_is_object) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( object(X2)
& object(X1)
& property(X0) )
=> ( ( X1 = X2
& is_the(X1,X0) )
<=> ? [X3] :
( X3 = X2
& ! [X4] :
( object(X4)
=> ( exemplifies_property(X0,X4)
=> X4 = X3 ) )
& exemplifies_property(X0,X3)
& object(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_axiom_identity_instance) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( ( object(X2)
& property(X1)
& object(X0) )
=> ( ( X0 = X2
& is_the(X0,X1) )
=> exemplifies_property(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( ( object(X2)
& property(X1)
& object(X0) )
=> ( ( X0 = X2
& is_the(X0,X1) )
=> exemplifies_property(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( ~ is_the(X0,X1)
| ( object(X0)
& property(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ object(X2)
| ~ object(X1)
| ~ property(X0)
| ( ( X1 = X2
& is_the(X1,X0) )
<=> ? [X3] :
( X3 = X2
& ! [X4] :
( ~ object(X4)
| ~ exemplifies_property(X0,X4)
| X4 = X3 )
& exemplifies_property(X0,X3)
& object(X3) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ object(X2)
| ~ object(X1)
| ~ property(X0)
| ( ( X1 = X2
& is_the(X1,X0) )
<=> ? [X3] :
( X3 = X2
& ! [X4] :
( ~ object(X4)
| ~ exemplifies_property(X0,X4)
| X4 = X3 )
& exemplifies_property(X0,X3)
& object(X3) ) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
? [X0,X1,X2] :
( object(X2)
& property(X1)
& object(X0)
& X0 = X2
& is_the(X0,X1)
& ~ exemplifies_property(X1,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0,X1,X2] :
( object(X2)
& property(X1)
& object(X0)
& X0 = X2
& is_the(X0,X1)
& ~ exemplifies_property(X1,X2) ),
inference(flattening,[],[f12]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ sP1(X2,X0,X1)
| ( ( X1 != X2
| ~ is_the(X1,X0)
| sP0(X0,X2) )
& ( ~ sP0(X0,X2)
| ( X1 = X2
& is_the(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ sP1(X2,X0,X1)
| ( ( X1 != X2
| ~ is_the(X1,X0)
| sP0(X0,X2) )
& ( ~ sP0(X0,X2)
| ( X1 = X2
& is_the(X1,X0) ) ) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ( ( X0 != X2
| ~ is_the(X2,X1)
| sP0(X1,X0) )
& ( ~ sP0(X1,X0)
| ( X0 = X2
& is_the(X2,X1) ) ) ) ),
inference(rectify,[],[f18]) ).
fof(f23,plain,
( object(sK6)
& property(sK5)
& object(sK4)
& sK4 = sK6
& is_the(sK4,sK5)
& ~ exemplifies_property(sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( ~ is_the(X0,X1)
| object(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1] :
( ~ is_the(X0,X1)
| property(X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| X0 != X2
| ~ is_the(X2,X1)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ object(X2)
| ~ object(X1)
| ~ property(X0)
| sP1(X2,X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
is_the(sK4,sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
~ exemplifies_property(sK5,sK6),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
is_the(sK6,sK5),
inference(definition_unfolding,[],[f44,f43]) ).
fof(f48,plain,
! [X2,X1] :
( ~ sP1(X2,X1,X2)
| ~ is_the(X2,X1)
| sP0(X1,X2) ),
inference(equality_resolution,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( property(X1)
| ~ is_the(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( object(X0)
| ~ is_the(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| ~ is_the(X0,X1)
| ~ sP1(X0,X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X0,X1)
| ~ object(X2)
| ~ object(X1)
| ~ property(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_65,negated_conjecture,
~ exemplifies_property(sK5,sK6),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,negated_conjecture,
is_the(sK6,sK5),
inference(cnf_transformation,[],[f46]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP0(X3,X0)
| ~ object(X2)
| ~ object(X1)
| ~ property(X4)
| ~ is_the(X0,X3)
| ( X3 != X4 )
| ( X0 != X2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_64]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| ~ object(X0)
| ~ property(X1)
| ~ is_the(X0,X1) ),
inference(unflattening,[status(thm)],[c_366]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| ~ is_the(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_367,c_53,c_52,c_367]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0)
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_369,c_66]) ).
tcf(c_391,plain,
sP0(sK5,sK6),
inference(unflattening,[status(thm)],[c_390]) ).
tcf(c_770,plain,
sP0(sK5,sK6),
inference(demodulation,[status(thm)],[c_391]) ).
tcf(c_773,negated_conjecture,
~ exemplifies_property(sK5,sK6),
inference(demodulation,[status(thm)],[c_65]) ).
fof(f14,definition,
! [X0,X2] :
( sP0(X0,X2)
<=> ? [X3] :
( X3 = X2
& ! [X4] :
( ~ object(X4)
| ~ exemplifies_property(X0,X4)
| X4 = X3 )
& exemplifies_property(X0,X3)
& object(X3) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f15,definition,
! [X2,X0,X1] :
( ~ sP1(X2,X0,X1)
| ( ( X1 = X2
& is_the(X1,X0) )
<=> sP0(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ object(X2)
| ~ object(X1)
| ~ property(X0)
| sP1(X2,X0,X1) ),
inference(definition_folding,[],[f11,f15,f14]) ).
fof(f20,plain,
! [X0,X2] :
( ( ~ sP0(X0,X2)
| ? [X3] :
( X3 = X2
& ! [X4] :
( ~ object(X4)
| ~ exemplifies_property(X0,X4)
| X4 = X3 )
& exemplifies_property(X0,X3)
& object(X3) ) )
& ( ! [X3] :
( X2 != X3
| ? [X4] :
( object(X4)
& exemplifies_property(X0,X4)
& X3 != X4 )
| ~ exemplifies_property(X0,X3)
| ~ object(X3) )
| sP0(X0,X2) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ sP0(X0,X1)
| ? [X4] :
( X1 = X4
& ! [X5] :
( ~ object(X5)
| ~ exemplifies_property(X0,X5)
| X4 = X5 )
& exemplifies_property(X0,X4)
& object(X4) ) )
& ( ! [X2] :
( X1 != X2
| ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& X2 != X3 )
| ~ exemplifies_property(X0,X2)
| ~ object(X2) )
| sP0(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ sP0(X0,X1)
| ( sK3(X0,X1) = X1
& ! [X5] :
( ~ object(X5)
| ~ exemplifies_property(X0,X5)
| sK3(X0,X1) = X5 )
& exemplifies_property(X0,sK3(X0,X1))
& object(sK3(X0,X1)) ) )
& ( ! [X2] :
( X1 != X2
| ( object(sK2(X0,X2))
& exemplifies_property(X0,sK2(X0,X2))
& sK2(X0,X2) != X2 )
| ~ exemplifies_property(X0,X2)
| ~ object(X2) )
| sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X2)),skolemize(X4,sK3(X0,X1))],[f21]) ).
fof(f32,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK3(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| exemplifies_property(X0,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( exemplifies_property(X0,sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( sK3(X0,X1) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_1037,plain,
sK3(sK5,sK6) = sK6,
inference(superposition,[status(thm)],[c_770,c_63]) ).
tcf(c_1060,plain,
( exemplifies_property(sK5,sK6)
| ~ sP0(sK5,sK6) ),
inference(superposition,[status(thm)],[c_1037,c_61]) ).
tcf(c_1062,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1060,c_773,c_770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI010+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 06:06:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.40
% 0.09/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.40
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 0.45/1.28 % SZS status Started for theBenchmark.p
% 0.45/1.28 % SZS status Theorem for theBenchmark.p
% 0.45/1.28
% 0.45/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.28
% 0.45/1.28 % ------ iProver source info
% 0.45/1.28
% 0.45/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.28 % git: non_committed_changes: false
% 0.45/1.28
% 0.45/1.28 % ------ Parsing...
% 0.45/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.28 % ------ Proving...
% 0.45/1.28 % ------ Problem Properties
% 0.45/1.28
% 0.45/1.28 %
% 0.45/1.28 % clauses 16
% 0.45/1.28 % conjectures 3
% 0.45/1.28 % EPR 9
% 0.45/1.28 % Horn 14
% 0.45/1.28 % unary 4
% 0.45/1.28 % binary 6
% 0.45/1.28 % lits 38
% 0.45/1.28 % lits eq 4
% 0.45/1.28 % fd_pure 0
% 0.45/1.28 % fd_pseudo 0
% 0.45/1.28 % fd_cond 0
% 0.45/1.28 % fd_pseudo_cond 2
% 0.45/1.28 % AC symbols 0
% 0.45/1.28
% 0.45/1.28 % ------ Schedule dynamic 5 is on
% 0.45/1.28
% 0.45/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 % ------
% 0.45/1.28 % Current options:
% 0.45/1.28 % ------
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 %
% 0.45/1.28
% 0.45/1.28 % ------ Proving...
% 0.45/1.28 %
% 0.45/1.28
% 0.45/1.28 % SZS status Theorem for theBenchmark.p
% 0.45/1.28
% 0.45/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.28
% 0.45/1.28
%------------------------------------------------------------------------------