%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET908+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 : 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 02:49:05 PM UTC 2026
% Result : Theorem 2.25s 1.31s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 22 unt; 2 def)
% Number of atoms : 156 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 170 ( 67 ~; 66 |; 32 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 74 !; 9 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f12,conjecture,
! [X0,X1] : set_union2(singleton(X0),X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : set_union2(singleton(X0),X1) != empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f18,plain,
? [X0,X1] : empty_set = set_union2(singleton(X0),X1),
inference(ennf_transformation,[],[f13]) ).
fof(f19,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,[],[f3]) ).
fof(f20,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,[],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f22,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK1(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f27]) ).
fof(f31,plain,
empty_set = set_union2(singleton(sK5),sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f18]) ).
fof(f33,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
empty_set = set_union2(singleton(sK5),sK6),
inference(cnf_transformation,[],[f31]) ).
fof(f53,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f35]) ).
fof(f54,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f53]) ).
fof(f56,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f38]) ).
fof(f57,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f42]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f56]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_69,negated_conjecture,
set_union2(singleton(sK5),sK6) = empty_set,
inference(cnf_transformation,[],[f52]) ).
tcf(c_171,plain,
set_union2(sK6,singleton(sK5)) = empty_set,
inference(demodulation,[status(thm)],[c_69,c_50]) ).
tcf(c_233,definition,
iPr_def_10 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_234,definition,
iPr_def_11 = set_union2(sK6,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_235,plain,
iPr_def_11 = empty_set,
inference(demodulation,[status(thm)],[c_171,c_233,c_234]) ).
tcf(c_485,plain,
! [X0: $i] : ~ in(X0,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_56,c_235]) ).
tcf(c_486,plain,
in(sK5,iPr_def_10),
inference(superposition,[status(thm)],[c_233,c_53]) ).
tcf(c_487,plain,
set_union2(iPr_def_10,sK6) = iPr_def_11,
inference(demodulation,[status(thm)],[c_234,c_50]) ).
tcf(c_570,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_487,c_60]) ).
tcf(c_573,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_570,c_485]) ).
tcf(c_576,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_486,c_573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:23:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 2.25/1.31 % SZS status Started for theBenchmark.p
% 2.25/1.31 % SZS status Theorem for theBenchmark.p
% 2.25/1.31
% 2.25/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.25/1.31
% 2.25/1.31 % ------ iProver source info
% 2.25/1.31
% 2.25/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.25/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.25/1.31 % git: non_committed_changes: false
% 2.25/1.31
% 2.25/1.31 % ------ Parsing...
% 2.25/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.25/1.31
% 2.25/1.31 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.25/1.31
% 2.25/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.25/1.31
% 2.25/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.25/1.31 % ------ Proving...
% 2.25/1.31 % ------ Problem Properties
% 2.25/1.31
% 2.25/1.31 %
% 2.25/1.31 % clauses 23
% 2.25/1.31 % conjectures 0
% 2.25/1.31 % EPR 6
% 2.25/1.31 % Horn 19
% 2.25/1.31 % unary 10
% 2.25/1.31 % binary 7
% 2.25/1.31 % lits 43
% 2.25/1.31 % lits eq 14
% 2.25/1.31 % fd_pure 0
% 2.25/1.31 % fd_pseudo 0
% 2.25/1.31 % fd_cond 1
% 2.25/1.31 % fd_pseudo_cond 5
% 2.25/1.31 % AC symbols 0
% 2.25/1.31
% 2.25/1.31 % ------ Schedule dynamic 5 is on
% 2.25/1.31
% 2.25/1.31 % ------ no conjectures: strip conj schedule
% 2.25/1.31
% 2.25/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.25/1.31
% 2.25/1.31
% 2.25/1.31 % ------
% 2.25/1.31 % Current options:
% 2.25/1.31 % ------
% 2.25/1.31
% 2.25/1.31
% 2.25/1.31 %
% 2.25/1.31
% 2.25/1.31 % ------ Proving...
% 2.25/1.31 %
% 2.25/1.31
% 2.25/1.31 % SZS status Theorem for theBenchmark.p
% 2.25/1.31
% 2.25/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.25/1.31
% 2.25/1.31
%------------------------------------------------------------------------------