%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:48:52 PM UTC 2026
% Result : Theorem 0.28s 1.09s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 11 unt; 3 def)
% Number of atoms : 138 ( 77 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 115 ( 49 ~; 48 |; 12 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 46 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f6,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<~> X0 != X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f11,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
? [X0,X1] :
( ( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
| X0 != X1 )
& ( singleton(X0) != set_difference(singleton(X0),singleton(X1))
| X0 = X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f17,plain,
( ( singleton(sK3) = set_difference(singleton(sK3),singleton(sK4))
| sK3 != sK4 )
& ( singleton(sK3) != set_difference(singleton(sK3),singleton(sK4))
| sK3 = sK4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f16]) ).
fof(f19,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X0,X1] :
( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( in(X0,X1)
| singleton(X0) = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
( singleton(sK3) = set_difference(singleton(sK3),singleton(sK4))
| sK3 != sK4 ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
( singleton(sK3) != set_difference(singleton(sK3),singleton(sK4))
| sK3 = sK4 ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f20]) ).
fof(f30,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f29]) ).
fof(f31,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ( set_difference(singleton(X0),X1) != singleton(X0) ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_58,negated_conjecture,
( ( sK3 = sK4 )
| ( set_difference(singleton(sK3),singleton(sK4)) != singleton(sK3) ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,negated_conjecture,
( ( set_difference(singleton(sK3),singleton(sK4)) = singleton(sK3) )
| ( sK3 != sK4 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_311,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_312,definition,
iPr_def_11 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_313,definition,
iPr_def_12 = set_difference(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_314,negated_conjecture,
( ( iPr_def_12 = iPr_def_10 )
| ( sK3 != sK4 ) ),
inference(demodulation,[status(thm)],[c_59,c_312,c_311,c_313]) ).
tcf(c_315,negated_conjecture,
( ( sK3 = sK4 )
| ( iPr_def_12 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_588,plain,
in(sK4,iPr_def_11),
inference(superposition,[status(thm)],[c_312,c_52]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( set_difference(singleton(X0),singleton(X1)) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_623,plain,
! [X0: $i] :
( ~ in(sK3,X0)
| ( set_difference(iPr_def_10,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_311,c_55]) ).
tcf(c_662,plain,
( ~ in(sK3,iPr_def_11)
| ( iPr_def_10 != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_313,c_623]) ).
tcf(c_688,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( set_difference(iPr_def_10,singleton(X0)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_311,c_614]) ).
tcf(c_748,plain,
( ( sK3 = sK4 )
| ( set_difference(iPr_def_10,iPr_def_11) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_312,c_688]) ).
tcf(c_752,plain,
( ( iPr_def_10 = iPr_def_12 )
| ( sK3 = sK4 ) ),
inference(light_normalisation,[status(thm)],[c_748,c_313]) ).
tcf(c_768,plain,
iPr_def_10 = iPr_def_12,
inference(superposition,[status(thm)],[c_752,c_314]) ).
tcf(c_769,plain,
~ in(sK3,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_662,c_768]) ).
tcf(c_771,plain,
( ( sK3 = sK4 )
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_315,c_768]) ).
tcf(c_773,plain,
sK3 = sK4,
inference(equality_resolution_simp,[status(thm)],[c_771]) ).
tcf(c_778,plain,
in(sK3,iPr_def_11),
inference(demodulation,[status(thm)],[c_588,c_773]) ).
tcf(c_781,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_778,c_769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 12:18:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.33 Running first-order theorem proving
% 0.03/0.33 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
% 0.03/0.34
% 0.03/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.34
% 0.08/0.34 % Detected problem language: tptp
% 0.08/0.36 % Proving...
% 0.28/1.09 % SZS status Started for theBenchmark.p
% 0.28/1.09 % SZS status Theorem for theBenchmark.p
% 0.28/1.09
% 0.28/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.28/1.09
% 0.28/1.09 % ------ iProver source info
% 0.28/1.09
% 0.28/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.28/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.28/1.09 % git: non_committed_changes: false
% 0.28/1.09
% 0.28/1.09 % ------ Parsing...
% 0.28/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.28/1.09
% 0.28/1.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.28/1.09
% 0.28/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.28/1.09
% 0.28/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.28/1.09 % ------ Proving...
% 0.28/1.09 % ------ Problem Properties
% 0.28/1.09
% 0.28/1.09 %
% 0.28/1.09 % clauses 13
% 0.28/1.09 % conjectures 2
% 0.28/1.09 % EPR 4
% 0.28/1.09 % Horn 11
% 0.28/1.09 % unary 5
% 0.28/1.09 % binary 6
% 0.28/1.09 % lits 23
% 0.28/1.09 % lits eq 15
% 0.28/1.09 % fd_pure 0
% 0.28/1.09 % fd_pseudo 0
% 0.28/1.09 % fd_cond 0
% 0.28/1.09 % fd_pseudo_cond 2
% 0.28/1.09 % AC symbols 0
% 0.28/1.09
% 0.28/1.09 % ------ Schedule dynamic 5 is on
% 0.28/1.09
% 0.28/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.28/1.09
% 0.28/1.09
% 0.28/1.09 % ------
% 0.28/1.09 % Current options:
% 0.28/1.09 % ------
% 0.28/1.09
% 0.28/1.09
% 0.28/1.09 %
% 0.28/1.09
% 0.28/1.09 % ------ Proving...
% 0.28/1.09 %
% 0.28/1.09
% 0.28/1.09 % SZS status Theorem for theBenchmark.p
% 0.28/1.09
% 0.28/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.28/1.09
% 0.28/1.09
%------------------------------------------------------------------------------