%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET027+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 02:46:10 PM UTC 2026
% Result : Theorem 0.21s 1.08s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 33 ~; 28 |; 14 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 39 !; 8 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f3,conjecture,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
fof(f4,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f6,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X1)
& ~ subset(X0,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f7,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X1)
& ~ subset(X0,X2) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f9]) ).
fof(f11,plain,
( subset(sK2,sK3)
& subset(sK1,sK2)
& ~ subset(sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f7]) ).
fof(f12,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
~ subset(sK1,sK3),
inference(cnf_transformation,[],[f11]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_53,negated_conjecture,
~ subset(sK1,sK3),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_100,plain,
member(sK0(sK1,sK3),sK1),
inference(resolution,[status(thm)],[c_50,c_53]) ).
tcf(c_104,plain,
~ member(sK0(sK1,sK3),sK3),
inference(resolution,[status(thm)],[c_49,c_53]) ).
tcf(c_141,plain,
! [X0: $i] :
( member(sK0(sK1,sK3),X0)
| ~ subset(sK1,X0)
| ~ member(sK0(sK1,sK3),sK1) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( member(sK0(sK1,sK3),X1)
| ~ subset(X0,X1)
| ~ member(sK0(sK1,sK3),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_145,plain,
! [X0: $i] :
( member(sK0(sK1,sK3),sK3)
| ~ subset(X0,sK3)
| ~ member(sK0(sK1,sK3),X0) ),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_149,plain,
( member(sK0(sK1,sK3),sK3)
| ~ subset(sK2,sK3)
| ~ member(sK0(sK1,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_150,plain,
( member(sK0(sK1,sK3),sK2)
| ~ subset(sK1,sK2)
| ~ member(sK0(sK1,sK3),sK1) ),
inference(instantiation,[status(thm)],[c_141]) ).
tcf(c_151,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_150,c_149,c_104,c_100,c_54,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET027+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.06/0.30 % Computer : n012.cluster.edu
% 0.06/0.30 % Model : x86_64 x86_64
% 0.06/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.30 % Memory : 8046.5625MB
% 0.06/0.30 % OS : Linux 6.8.0-71-generic
% 0.06/0.30 % CPULimit : 300
% 0.06/0.30 % WCLimit : 300
% 0.06/0.30 % DateTime : Thu Sep 24 09:16:20 UTC 2026
% 0.06/0.31 % CPUTime :
% 0.06/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.06/0.33 Running first-order theorem proving
% 0.06/0.33 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
% 0.08/0.34
% 0.08/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.34
% 0.08/0.34 % Detected problem language: tptp
% 0.08/0.34 % Proving...
% 0.21/1.08 % SZS status Started for theBenchmark.p
% 0.21/1.08 % SZS status Theorem for theBenchmark.p
% 0.21/1.08
% 0.21/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.21/1.08
% 0.21/1.08 % ------ iProver source info
% 0.21/1.08
% 0.21/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.21/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.21/1.08 % git: non_committed_changes: false
% 0.21/1.08
% 0.21/1.08 % ------ Parsing...
% 0.21/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.21/1.08
% 0.21/1.08 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.21/1.08
% 0.21/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.21/1.08 % ------ Proving...
% 0.21/1.08 % ------ Problem Properties
% 0.21/1.08
% 0.21/1.08 %
% 0.21/1.08 % clauses 7
% 0.21/1.08 % conjectures 3
% 0.21/1.08 % EPR 5
% 0.21/1.08 % Horn 6
% 0.21/1.08 % unary 4
% 0.21/1.08 % binary 2
% 0.21/1.08 % lits 11
% 0.21/1.08 % lits eq 0
% 0.21/1.08 % fd_pure 0
% 0.21/1.08 % fd_pseudo 0
% 0.21/1.08 % fd_cond 0
% 0.21/1.08 % fd_pseudo_cond 0
% 0.21/1.08 % AC symbols 0
% 0.21/1.08
% 0.21/1.08 % ------ Schedule dynamic 5 is on
% 0.21/1.08
% 0.21/1.08 % ------ no equalities: superposition off
% 0.21/1.08
% 0.21/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.21/1.08
% 0.21/1.08
% 0.21/1.08 % ------
% 0.21/1.08 % Current options:
% 0.21/1.08 % ------
% 0.21/1.08
% 0.21/1.08
% 0.21/1.08 %
% 0.21/1.08
% 0.21/1.08 % ------ Proving...
% 0.21/1.08 %
% 0.21/1.08
% 0.21/1.08 % SZS status Theorem for theBenchmark.p
% 0.21/1.08
% 0.21/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.21/1.08
% 0.21/1.08
%------------------------------------------------------------------------------