%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET929+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 : n002.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 02:49:08 PM UTC 2026
% Result : Theorem 1.22s 1.29s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 3 unt; 0 def)
% Number of atoms : 131 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 59 ~; 63 |; 15 &)
% ( 4 <=>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 87 !; 9 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<=> ( in(X1,X2)
& in(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<~> ( in(X1,X2)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = empty_set
| ( in(X1,X2)
& in(X0,X2) ) )
& ( empty_set != set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = empty_set
| ( in(X1,X2)
& in(X0,X2) ) )
& ( empty_set != set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ( empty_set = set_difference(unordered_pair(sK2,sK3),sK4)
| ( in(sK3,sK4)
& in(sK2,sK4) ) )
& ( empty_set != set_difference(unordered_pair(sK2,sK3),sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
( empty_set = set_difference(unordered_pair(sK2,sK3),sK4)
| in(sK3,sK4) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
( empty_set = set_difference(unordered_pair(sK2,sK3),sK4)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
( empty_set != set_difference(unordered_pair(sK2,sK3),sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X2,X0),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_60,negated_conjecture,
( ~ in(sK3,sK4)
| ~ in(sK2,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) != empty_set ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,negated_conjecture,
( in(sK2,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) = empty_set ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,negated_conjecture,
( in(sK3,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) = empty_set ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) != empty_set )
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(renaming,[status(thm)],[c_68]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_76]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_78]) ).
tcf(c_84,plain,
( ( set_difference(unordered_pair(sK2,sK3),sK4) = empty_set )
| in(sK2,sK4) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_85,plain,
( in(sK2,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) = empty_set ) ),
inference(renaming,[status(thm)],[c_84]) ).
tcf(c_86,plain,
( ( set_difference(unordered_pair(sK2,sK3),sK4) = empty_set )
| in(sK3,sK4) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_87,plain,
( in(sK3,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) = empty_set ) ),
inference(renaming,[status(thm)],[c_86]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_difference(X2,X3) = empty_set )
| ~ in(X1,X4)
| ~ in(X0,X4)
| ( X3 != X4 )
| ( unordered_pair(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_57]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X2),X1) = empty_set )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(unflattening,[status(thm)],[c_241]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X3,X4)
| ( X1 != X4 )
| ( set_difference(X0,X1) != empty_set )
| ( unordered_pair(X2,X3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_77]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ( set_difference(unordered_pair(X0,X1),X2) != empty_set ) ),
inference(unflattening,[status(thm)],[c_252]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,X4)
| ( X1 != X4 )
| ( set_difference(X0,X1) != empty_set )
| ( unordered_pair(X2,X3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_79]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ( set_difference(unordered_pair(X0,X1),X2) != empty_set ) ),
inference(unflattening,[status(thm)],[c_261]) ).
tcf(c_303,plain,
( ~ in(sK3,sK4)
| ~ in(sK2,sK4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_242]) ).
tcf(c_305,plain,
in(sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_87,c_253]) ).
tcf(c_308,plain,
in(sK2,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_85,c_262]) ).
tcf(c_310,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_308,c_305,c_303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:26:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.22/1.29 % SZS status Started for theBenchmark.p
% 1.22/1.29 % SZS status Theorem for theBenchmark.p
% 1.22/1.29
% 1.22/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.22/1.29
% 1.22/1.29 % ------ iProver source info
% 1.22/1.29
% 1.22/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.22/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.22/1.29 % git: non_committed_changes: false
% 1.22/1.29
% 1.22/1.29 % ------ Parsing...
% 1.22/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.22/1.29
% 1.22/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s %
% 1.22/1.29
% 1.22/1.29 % SZS status Theorem for theBenchmark.p
% 1.22/1.29
% 1.22/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.22/1.29
% 1.22/1.29
%------------------------------------------------------------------------------