%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET921+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 : n019.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 02:49:07 PM UTC 2026
% Result : Theorem 2.26s 1.33s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 12 unt; 2 def)
% Number of atoms : 221 ( 60 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 242 ( 96 ~; 100 |; 39 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 85 !; 14 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<~> ( X0 != X2
& in(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,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f15]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( in(X0,set_difference(X1,singleton(X2)))
| ( X0 != X2
& in(X0,X1) ) )
& ( ~ in(X0,set_difference(X1,singleton(X2)))
| X0 = X2
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( in(X0,set_difference(X1,singleton(X2)))
| ( X0 != X2
& in(X0,X1) ) )
& ( ~ in(X0,set_difference(X1,singleton(X2)))
| X0 = X2
| ~ in(X0,X1) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ( in(sK4,set_difference(sK5,singleton(sK6)))
| ( sK4 != sK6
& in(sK4,sK5) ) )
& ( ~ in(sK4,set_difference(sK5,singleton(sK6)))
| sK4 = sK6
| ~ in(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f20]) ).
fof(f23,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
( in(sK4,set_difference(sK5,singleton(sK6)))
| sK4 != sK6 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
( in(sK4,set_difference(sK5,singleton(sK6)))
| in(sK4,sK5) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
( ~ in(sK4,set_difference(sK5,singleton(sK6)))
| sK4 = sK6
| ~ in(sK4,sK5) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f24]) ).
fof(f39,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f38]) ).
fof(f40,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f23]) ).
fof(f41,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f29]) ).
fof(f42,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f28]) ).
fof(f43,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_62,negated_conjecture,
( ( sK4 = sK6 )
| ~ in(sK4,sK5)
| ~ in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_63,negated_conjecture,
( in(sK4,sK5)
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_64,negated_conjecture,
( in(sK4,set_difference(sK5,singleton(sK6)))
| ( sK4 != sK6 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_89,plain,
in(sK4,sK5),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_58]) ).
tcf(c_218,plain,
( ( sK4 = sK6 )
| ~ in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(prop_impl_just,[status(thm)],[c_62,c_89]) ).
tcf(c_400,definition,
iPr_def_10 = singleton(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_401,definition,
iPr_def_11 = set_difference(sK5,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_402,plain,
in(sK4,sK5),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_403,negated_conjecture,
( in(sK4,iPr_def_11)
| ( sK4 != sK6 ) ),
inference(demodulation,[status(thm)],[c_64,c_400,c_401]) ).
tcf(c_614,plain,
in(sK6,iPr_def_10),
inference(superposition,[status(thm)],[c_400,c_52]) ).
tcf(c_623,plain,
( ( sK4 = sK6 )
| ~ in(sK4,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_218,c_400,c_401]) ).
tcf(c_635,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_400,c_53]) ).
tcf(c_638,plain,
( ( sK4 = sK6 )
| ~ in(sK4,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_635]) ).
tcf(c_650,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_401,c_59]) ).
tcf(c_660,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(X0,iPr_def_10)
| ~ in(X0,sK5) ),
inference(superposition,[status(thm)],[c_401,c_57]) ).
tcf(c_670,plain,
( in(sK4,iPr_def_11)
| in(sK4,iPr_def_10)
| ~ in(sK4,sK5) ),
inference(instantiation,[status(thm)],[c_660]) ).
tcf(c_688,plain,
~ in(sK6,iPr_def_11),
inference(superposition,[status(thm)],[c_614,c_650]) ).
tcf(c_695,plain,
( in(sK4,iPr_def_11)
| in(sK4,iPr_def_10) ),
inference(superposition,[status(thm)],[c_402,c_660]) ).
tcf(c_698,plain,
in(sK4,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_695,c_89,c_403,c_638,c_670]) ).
tcf(c_700,plain,
sK4 = sK6,
inference(backward_subsumption_resolution,[status(thm)],[c_623,c_698]) ).
tcf(c_701,plain,
~ in(sK4,iPr_def_11),
inference(demodulation,[status(thm)],[c_688,c_700]) ).
tcf(c_708,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_701,c_698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:23:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.45
% 0.14/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.45
% 0.14/0.45 % Detected problem language: tptp
% 0.14/0.47 % Proving...
% 2.26/1.33 % SZS status Started for theBenchmark.p
% 2.26/1.33 % SZS status Theorem for theBenchmark.p
% 2.26/1.33
% 2.26/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.26/1.33
% 2.26/1.33 % ------ iProver source info
% 2.26/1.33
% 2.26/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 2.26/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.26/1.33 % git: non_committed_changes: false
% 2.26/1.33
% 2.26/1.33 % ------ Parsing...
% 2.26/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.26/1.33
% 2.26/1.33 % ------ 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 %
% 2.26/1.33
% 2.26/1.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.26/1.33
% 2.26/1.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.26/1.33 % ------ Proving...
% 2.26/1.33 % ------ Problem Properties
% 2.26/1.33
% 2.26/1.33 %
% 2.26/1.33 % clauses 17
% 2.26/1.33 % conjectures 1
% 2.26/1.33 % EPR 4
% 2.26/1.33 % Horn 12
% 2.26/1.33 % unary 5
% 2.26/1.33 % binary 6
% 2.26/1.33 % lits 36
% 2.26/1.33 % lits eq 13
% 2.26/1.33 % fd_pure 0
% 2.26/1.33 % fd_pseudo 0
% 2.26/1.33 % fd_cond 0
% 2.26/1.33 % fd_pseudo_cond 5
% 2.26/1.33 % AC symbols 0
% 2.26/1.33
% 2.26/1.33 % ------ Schedule dynamic 5 is on
% 2.26/1.33
% 2.26/1.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.26/1.33
% 2.26/1.33
% 2.26/1.33 % ------
% 2.26/1.33 % Current options:
% 2.26/1.33 % ------
% 2.26/1.33
% 2.26/1.33
% 2.26/1.33 %
% 2.26/1.33
% 2.26/1.33 % ------ Proving...
% 2.26/1.33 %
% 2.26/1.33
% 2.26/1.33 % SZS status Theorem for theBenchmark.p
% 2.26/1.33
% 2.26/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.26/1.33
% 2.26/1.33
%------------------------------------------------------------------------------