%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 02:49:04 PM UTC 2026
% Result : Theorem 0.56s 1.36s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 11 unt; 1 def)
% Number of atoms : 72 ( 54 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 38 ~; 23 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 30 !; 3 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1] :
~ ( ! [X2] :
~ ( X2 != X1
& in(X2,X0) )
& X0 != empty_set
& X0 != singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
~ ( ! [X2] :
~ ( X2 != X1
& in(X2,X0) )
& X0 != empty_set
& X0 != singleton(X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( X2 != X1
& in(X2,X0) )
& X0 != empty_set
& X0 != singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_zfmisc_1) ).
fof(f9,plain,
? [X0,X1] :
( ! [X2] :
( X1 = X2
| ~ in(X2,X0) )
& X0 != empty_set
& X0 != singleton(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( ? [X2] :
( X2 != X1
& in(X2,X0) )
| empty_set = X0
| singleton(X1) = X0 ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
( ! [X2] :
( sK3 = X2
| ~ in(X2,sK2) )
& empty_set != sK2
& sK2 != singleton(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( ( sK4(X0,X1) != X1
& in(sK4(X0,X1),X0) )
| empty_set = X0
| singleton(X1) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f10]) ).
fof(f19,plain,
! [X2] :
( sK3 = X2
| ~ in(X2,sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
sK2 != singleton(sK3),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( sK4(X0,X1) != X1
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_53,negated_conjecture,
singleton(sK3) != sK2,
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,negated_conjecture,
empty_set != sK2,
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( ( X0 = sK3 )
| ~ in(X0,sK2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(sK4(X1,X0),X1)
| ( X1 = empty_set )
| ( singleton(X0) = X1 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ( sK4(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_126,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_127,negated_conjecture,
! [X0: $i] :
( ( X0 = sK3 )
| ~ in(X0,sK2) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_128,negated_conjecture,
empty_set != sK2,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_129,negated_conjecture,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_53,c_126]) ).
tcf(c_276,plain,
! [X0: $i] :
( ( empty_set = sK2 )
| ( singleton(X0) = sK2 )
| ( sK4(sK2,X0) = sK3 ) ),
inference(superposition,[status(thm)],[c_56,c_127]) ).
tcf(c_277,plain,
! [X0: $i] :
( ( singleton(X0) = sK2 )
| ( sK4(sK2,X0) = sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_276,c_128]) ).
tcf(c_289,plain,
! [X0: $i] :
( ( empty_set = sK2 )
| ( singleton(X0) = sK2 )
| ( X0 != sK3 ) ),
inference(superposition,[status(thm)],[c_277,c_57]) ).
tcf(c_293,plain,
! [X0: $i] :
( ( singleton(X0) = sK2 )
| ( X0 != sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_289,c_128]) ).
tcf(c_315,plain,
singleton(sK3) = sK2,
inference(equality_resolution,[status(thm)],[c_293]) ).
tcf(c_316,plain,
sK2 = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_315,c_126]) ).
tcf(c_322,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_129,c_316]) ).
tcf(c_324,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n018.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 12:23:07 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 0.14/0.48
% 0.14/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.48
% 0.14/0.49 % Detected problem language: tptp
% 0.22/0.50 % Proving...
% 0.56/1.36 % SZS status Started for theBenchmark.p
% 0.56/1.36 % SZS status Theorem for theBenchmark.p
% 0.56/1.36
% 0.56/1.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.56/1.36
% 0.56/1.36 % ------ iProver source info
% 0.56/1.36
% 0.56/1.36 % git: date: 2026-07-19 20:42:38 +0200
% 0.56/1.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.56/1.36 % git: non_committed_changes: false
% 0.56/1.36
% 0.56/1.36 % ------ Parsing...
% 0.56/1.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.56/1.36
% 0.56/1.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.56/1.36
% 0.56/1.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.56/1.36
% 0.56/1.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.56/1.36 % ------ Proving...
% 0.56/1.36 % ------ Problem Properties
% 0.56/1.36
% 0.56/1.36 %
% 0.56/1.36 % clauses 10
% 0.56/1.36 % conjectures 3
% 0.56/1.36 % EPR 7
% 0.56/1.36 % Horn 8
% 0.56/1.36 % unary 6
% 0.56/1.36 % binary 2
% 0.56/1.36 % lits 16
% 0.56/1.36 % lits eq 9
% 0.56/1.36 % fd_pure 0
% 0.56/1.36 % fd_pseudo 0
% 0.56/1.36 % fd_cond 1
% 0.56/1.36 % fd_pseudo_cond 2
% 0.56/1.36 % AC symbols 0
% 0.56/1.36
% 0.56/1.36 % ------ Schedule dynamic 5 is on
% 0.56/1.36
% 0.56/1.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.56/1.36
% 0.56/1.36
% 0.56/1.36 % ------
% 0.56/1.36 % Current options:
% 0.56/1.36 % ------
% 0.56/1.36
% 0.56/1.36
% 0.56/1.36 %
% 0.56/1.36
% 0.56/1.36 % ------ Proving...
% 0.56/1.36 %
% 0.56/1.36
% 0.56/1.36 % SZS status Theorem for theBenchmark.p
% 0.56/1.36
% 0.56/1.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.56/1.37
% 0.56/1.37
%------------------------------------------------------------------------------