%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET873+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 : n005.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 02:48:51 PM UTC 2026
% Result : Theorem 0.26s 1.05s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 20 unt; 3 def)
% Number of atoms : 101 ( 52 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 81 ( 34 ~; 31 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% 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 : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 1 sgn 50 !; 4 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( subset(set_union2(singleton(X0),X1),X1)
=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f19,plain,
? [X0,X1] :
( set_union2(singleton(X0),singleton(X1)) = singleton(X0)
& X0 != X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f25,plain,
( singleton(sK3) = set_union2(singleton(sK3),singleton(sK4))
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f19]) ).
fof(f27,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(set_union2(singleton(X0),X1),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
singleton(sK3) = set_union2(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f28]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,negated_conjecture,
set_union2(singleton(sK3),singleton(sK4)) = singleton(sK3),
inference(cnf_transformation,[],[f39]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ( X1 != X2 )
| ( set_union2(singleton(X0),X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_61]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_union2(singleton(X0),X1) != X1 ) ),
inference(unflattening,[status(thm)],[c_160]) ).
tcf(c_254,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_255,definition,
iPr_def_11 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_256,definition,
iPr_def_12 = set_union2(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_257,negated_conjecture,
iPr_def_12 = iPr_def_10,
inference(demodulation,[status(thm)],[c_63,c_255,c_254,c_256]) ).
tcf(c_258,negated_conjecture,
sK3 != sK4,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_441,plain,
set_union2(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_256,c_257]) ).
tcf(c_477,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_254,c_54]) ).
tcf(c_502,plain,
! [X0: $i] :
( in(sK4,X0)
| ( set_union2(iPr_def_11,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_255,c_161]) ).
tcf(c_563,plain,
! [X0: $i] :
( in(sK4,X0)
| ( set_union2(X0,iPr_def_11) != X0 ) ),
inference(superposition,[status(thm)],[c_50,c_502]) ).
tcf(c_583,plain,
in(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_441,c_563]) ).
tcf(c_585,plain,
sK3 = sK4,
inference(superposition,[status(thm)],[c_583,c_477]) ).
tcf(c_586,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_585,c_258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:18:03 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 0.26/1.05 % SZS status Started for theBenchmark.p
% 0.26/1.05 % SZS status Theorem for theBenchmark.p
% 0.26/1.05
% 0.26/1.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.26/1.05
% 0.26/1.05 % ------ iProver source info
% 0.26/1.05
% 0.26/1.05 % git: date: 2026-07-19 20:42:38 +0200
% 0.26/1.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.26/1.05 % git: non_committed_changes: false
% 0.26/1.05
% 0.26/1.05 % ------ Parsing...
% 0.26/1.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.26/1.05
% 0.26/1.05 % ------ 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 %
% 0.26/1.05
% 0.26/1.05 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.26/1.05
% 0.26/1.05 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.26/1.05 % ------ Proving...
% 0.26/1.05 % ------ Problem Properties
% 0.26/1.05
% 0.26/1.05 %
% 0.26/1.05 % clauses 17
% 0.26/1.05 % conjectures 2
% 0.26/1.05 % EPR 5
% 0.26/1.05 % Horn 16
% 0.26/1.05 % unary 10
% 0.26/1.05 % binary 5
% 0.26/1.05 % lits 26
% 0.26/1.05 % lits eq 13
% 0.26/1.05 % fd_pure 0
% 0.26/1.05 % fd_pseudo 0
% 0.26/1.05 % fd_cond 0
% 0.26/1.05 % fd_pseudo_cond 2
% 0.26/1.05 % AC symbols 0
% 0.26/1.05
% 0.26/1.05 % ------ Schedule dynamic 5 is on
% 0.26/1.05
% 0.26/1.05 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.26/1.05
% 0.26/1.05
% 0.26/1.05 % ------
% 0.26/1.05 % Current options:
% 0.26/1.05 % ------
% 0.26/1.05
% 0.26/1.05
% 0.26/1.05 %
% 0.26/1.05
% 0.26/1.05 % ------ Proving...
% 0.26/1.05 %
% 0.26/1.05
% 0.26/1.05 % SZS status Theorem for theBenchmark.p
% 0.26/1.05
% 0.26/1.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.26/1.05
% 0.26/1.05
%------------------------------------------------------------------------------