%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PHI012+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 : 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 02:30:29 PM UTC 2026
% Result : Theorem 0.56s 1.28s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 8 unt; 0 def)
% Number of atoms : 226 ( 26 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 298 ( 121 ~; 118 |; 46 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn 56 !; 16 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( object(X0)
=> ( exemplifies_property(none_greater,X0)
<=> ( ~ ? [X1] :
( exemplifies_property(conceivable,X1)
& exemplifies_relation(greater_than,X1,X0)
& object(X1) )
& exemplifies_property(conceivable,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_none_greater) ).
fof(f2,axiom,
! [X0,X1] :
( ( object(X1)
& object(X0) )
=> ( X0 = X1
| exemplifies_relation(greater_than,X1,X0)
| exemplifies_relation(greater_than,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_of_greater_than) ).
fof(f3,conjecture,
( ? [X0] :
( exemplifies_property(none_greater,X0)
& object(X0) )
=> ? [X0] :
( ! [X1] :
( object(X1)
=> ( exemplifies_property(none_greater,X1)
=> X1 = X0 ) )
& exemplifies_property(none_greater,X0)
& object(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2) ).
fof(f4,negated_conjecture,
~ ( ? [X0] :
( exemplifies_property(none_greater,X0)
& object(X0) )
=> ? [X0] :
( ! [X1] :
( object(X1)
=> ( exemplifies_property(none_greater,X1)
=> X1 = X0 ) )
& exemplifies_property(none_greater,X0)
& object(X0) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ( ? [X0] :
( exemplifies_property(none_greater,X0)
& object(X0) )
=> ? [X1] :
( ! [X2] :
( object(X2)
=> ( exemplifies_property(none_greater,X2)
=> X1 = X2 ) )
& exemplifies_property(none_greater,X1)
& object(X1) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
! [X0] :
( ~ object(X0)
| ( exemplifies_property(none_greater,X0)
<=> ( ! [X1] :
( ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_relation(greater_than,X1,X0)
| ~ object(X1) )
& exemplifies_property(conceivable,X0) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( ~ object(X1)
| ~ object(X0)
| X0 = X1
| exemplifies_relation(greater_than,X1,X0)
| exemplifies_relation(greater_than,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0,X1] :
( ~ object(X1)
| ~ object(X0)
| X0 = X1
| exemplifies_relation(greater_than,X1,X0)
| exemplifies_relation(greater_than,X0,X1) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ? [X0] :
( exemplifies_property(none_greater,X0)
& object(X0) )
& ! [X1] :
( ? [X2] :
( object(X2)
& exemplifies_property(none_greater,X2)
& X1 != X2 )
| ~ exemplifies_property(none_greater,X1)
| ~ object(X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
( ? [X0] :
( exemplifies_property(none_greater,X0)
& object(X0) )
& ! [X1] :
( ? [X2] :
( object(X2)
& exemplifies_property(none_greater,X2)
& X1 != X2 )
| ~ exemplifies_property(none_greater,X1)
| ~ object(X1) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ object(X0)
| ( ( ~ exemplifies_property(none_greater,X0)
| ( ! [X1] :
( ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_relation(greater_than,X1,X0)
| ~ object(X1) )
& exemplifies_property(conceivable,X0) ) )
& ( ? [X1] :
( exemplifies_property(conceivable,X1)
& exemplifies_relation(greater_than,X1,X0)
& object(X1) )
| ~ exemplifies_property(conceivable,X0)
| exemplifies_property(none_greater,X0) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0] :
( ~ object(X0)
| ( ( ~ exemplifies_property(none_greater,X0)
| ( ! [X1] :
( ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_relation(greater_than,X1,X0)
| ~ object(X1) )
& exemplifies_property(conceivable,X0) ) )
& ( ? [X1] :
( exemplifies_property(conceivable,X1)
& exemplifies_relation(greater_than,X1,X0)
& object(X1) )
| ~ exemplifies_property(conceivable,X0)
| exemplifies_property(none_greater,X0) ) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ object(X0)
| ( ( ~ exemplifies_property(none_greater,X0)
| ( ! [X2] :
( ~ exemplifies_property(conceivable,X2)
| ~ exemplifies_relation(greater_than,X2,X0)
| ~ object(X2) )
& exemplifies_property(conceivable,X0) ) )
& ( ? [X1] :
( exemplifies_property(conceivable,X1)
& exemplifies_relation(greater_than,X1,X0)
& object(X1) )
| ~ exemplifies_property(conceivable,X0)
| exemplifies_property(none_greater,X0) ) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ object(X0)
| ( ( ~ exemplifies_property(none_greater,X0)
| ( ! [X2] :
( ~ exemplifies_property(conceivable,X2)
| ~ exemplifies_relation(greater_than,X2,X0)
| ~ object(X2) )
& exemplifies_property(conceivable,X0) ) )
& ( ( exemplifies_property(conceivable,sK0(X0))
& exemplifies_relation(greater_than,sK0(X0),X0)
& object(sK0(X0)) )
| ~ exemplifies_property(conceivable,X0)
| exemplifies_property(none_greater,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f13]) ).
fof(f15,plain,
( ? [X2] :
( exemplifies_property(none_greater,X2)
& object(X2) )
& ! [X0] :
( ? [X1] :
( object(X1)
& exemplifies_property(none_greater,X1)
& X0 != X1 )
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ) ),
inference(rectify,[],[f10]) ).
fof(f16,plain,
( exemplifies_property(none_greater,sK2)
& object(sK2)
& ! [X0] :
( ( object(sK1(X0))
& exemplifies_property(none_greater,sK1(X0))
& sK1(X0) != X0 )
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2)],[f15]) ).
fof(f17,plain,
! [X2,X0] :
( ~ object(X0)
| ~ exemplifies_property(none_greater,X0)
| ~ exemplifies_property(conceivable,X2)
| ~ exemplifies_relation(greater_than,X2,X0)
| ~ object(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0] :
( ~ object(X0)
| ~ exemplifies_property(none_greater,X0)
| exemplifies_property(conceivable,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( ~ object(X1)
| ~ object(X0)
| X0 = X1
| exemplifies_relation(greater_than,X1,X0)
| exemplifies_relation(greater_than,X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
exemplifies_property(none_greater,sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
object(sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] :
( object(sK1(X0))
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0] :
( exemplifies_property(none_greater,sK1(X0))
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0] :
( sK1(X0) != X0
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_52,plain,
! [X0: $i] :
( exemplifies_property(conceivable,X0)
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ~ object(X1)
| ~ object(X0)
| ~ exemplifies_property(conceivable,X0)
| ~ exemplifies_property(none_greater,X1)
| ~ exemplifies_relation(greater_than,X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( exemplifies_relation(greater_than,X1,X0)
| exemplifies_relation(greater_than,X0,X1)
| ( X0 = X1 )
| ~ object(X1)
| ~ object(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( ~ object(X0)
| ~ exemplifies_property(none_greater,X0)
| ( sK1(X0) != X0 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( exemplifies_property(none_greater,sK1(X0))
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( object(sK1(X0))
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_58,negated_conjecture,
object(sK2),
inference(cnf_transformation,[],[f24]) ).
tcf(c_59,negated_conjecture,
exemplifies_property(none_greater,sK2),
inference(cnf_transformation,[],[f23]) ).
tcf(c_212,negated_conjecture,
exemplifies_property(none_greater,sK2),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_213,negated_conjecture,
object(sK2),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_215,negated_conjecture,
! [X0: $i] :
( exemplifies_property(none_greater,sK1(X0))
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_216,negated_conjecture,
! [X0: $i] :
( ~ object(X0)
| ~ exemplifies_property(none_greater,X0)
| ( sK1(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i] :
( exemplifies_relation(greater_than,X0,X1)
| ( X0 = X1 )
| ~ object(X1)
| ~ object(X0)
| ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_property(none_greater,X0) ),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_584,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ object(X1)
| ~ object(X0)
| ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_property(conceivable,X0)
| ~ exemplifies_property(none_greater,X1)
| ~ exemplifies_property(none_greater,X0) ),
inference(superposition,[status(thm)],[c_549,c_53]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ object(X1)
| ~ object(X0)
| ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_property(none_greater,X0)
| ~ exemplifies_property(none_greater,X1) ),
inference(global_subsumption_just,[status(thm)],[c_584,c_52,c_584]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ object(X1)
| ~ object(X0)
| ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_property(none_greater,X1)
| ~ exemplifies_property(none_greater,X0) ),
inference(renaming,[status(thm)],[c_592]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ object(X1)
| ~ object(X0)
| ~ exemplifies_property(none_greater,X1)
| ~ exemplifies_property(none_greater,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_593,c_52]) ).
tcf(c_617,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ object(sK2)
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(superposition,[status(thm)],[c_212,c_600]) ).
tcf(c_618,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_617,c_213]) ).
tcf(c_636,plain,
! [X0: $i] :
( ( sK1(X0) = sK2 )
| ~ object(X0)
| ~ object(sK1(X0))
| ~ exemplifies_property(none_greater,X0) ),
inference(superposition,[status(thm)],[c_215,c_618]) ).
tcf(c_643,plain,
! [X0: $i] :
( ( sK1(X0) = sK2 )
| ~ object(X0)
| ~ exemplifies_property(none_greater,X0) ),
inference(global_subsumption_just,[status(thm)],[c_636,c_57,c_636]) ).
tcf(c_653,plain,
( ( sK1(sK2) = sK2 )
| ~ object(sK2) ),
inference(superposition,[status(thm)],[c_212,c_643]) ).
tcf(c_654,plain,
sK1(sK2) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_653,c_213]) ).
tcf(c_664,plain,
( ~ object(sK2)
| ~ exemplifies_property(none_greater,sK2) ),
inference(superposition,[status(thm)],[c_654,c_216]) ).
tcf(c_666,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_664,c_213,c_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI012+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 06:05:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.56/1.28 % SZS status Started for theBenchmark.p
% 0.56/1.28 % SZS status Theorem for theBenchmark.p
% 0.56/1.28
% 0.56/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.56/1.28
% 0.56/1.28 % ------ iProver source info
% 0.56/1.28
% 0.56/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.56/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.56/1.28 % git: non_committed_changes: false
% 0.56/1.28
% 0.56/1.28 % ------ Parsing...
% 0.56/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.56/1.28
% 0.56/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.56/1.28
% 0.56/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.56/1.28
% 0.56/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.56/1.28 % ------ Proving...
% 0.56/1.28 % ------ Problem Properties
% 0.56/1.28
% 0.56/1.28 %
% 0.56/1.28 % clauses 11
% 0.56/1.28 % conjectures 5
% 0.56/1.28 % EPR 5
% 0.56/1.28 % Horn 7
% 0.56/1.28 % unary 2
% 0.56/1.28 % binary 0
% 0.56/1.28 % lits 36
% 0.56/1.28 % lits eq 2
% 0.56/1.28 % fd_pure 0
% 0.56/1.28 % fd_pseudo 0
% 0.56/1.28 % fd_cond 0
% 0.56/1.28 % fd_pseudo_cond 1
% 0.56/1.28 % AC symbols 0
% 0.56/1.28
% 0.56/1.28 % ------ Schedule dynamic 5 is on
% 0.56/1.28
% 0.56/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.56/1.28
% 0.56/1.28
% 0.56/1.28 % ------
% 0.56/1.28 % Current options:
% 0.56/1.28 % ------
% 0.56/1.28
% 0.56/1.28
% 0.56/1.28 %
% 0.56/1.28
% 0.56/1.28 % ------ Proving...
% 0.56/1.28 %
% 0.56/1.28
% 0.56/1.28 % SZS status Theorem for theBenchmark.p
% 0.56/1.28
% 0.56/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.56/1.28
% 0.56/1.28
%------------------------------------------------------------------------------