%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU149+3 : 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 : n015.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 02:55:36 PM UTC 2026
% Result : Theorem 1.80s 1.29s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 14 unt; 2 def)
% Number of atoms : 136 ( 89 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 153 ( 57 ~; 59 |; 31 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 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 : 65 ( 0 sgn 57 !; 8 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
& X0 != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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(f12,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,[],[f11]) ).
fof(f13,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))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0 )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f16]) ).
fof(f20,plain,
( singleton(sK4) = unordered_pair(sK5,sK6)
& sK4 != sK5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f10]) ).
fof(f23,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
singleton(sK4) = unordered_pair(sK5,sK6),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f23]) ).
fof(f40,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f29]) ).
fof(f41,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_63,negated_conjecture,
sK4 != sK5,
inference(cnf_transformation,[],[f36]) ).
tcf(c_64,negated_conjecture,
unordered_pair(sK5,sK6) = singleton(sK4),
inference(cnf_transformation,[],[f35]) ).
tcf(c_303,definition,
iPr_def_10 = unordered_pair(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_304,definition,
iPr_def_11 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_305,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_64,c_304,c_303]) ).
tcf(c_306,negated_conjecture,
sK4 != sK5,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_498,plain,
singleton(sK4) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_304,c_305]) ).
tcf(c_501,plain,
in(sK5,iPr_def_10),
inference(superposition,[status(thm)],[c_303,c_58]) ).
tcf(c_519,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_498,c_54]) ).
tcf(c_545,plain,
sK4 = sK5,
inference(superposition,[status(thm)],[c_501,c_519]) ).
tcf(c_546,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_545,c_306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU149+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 13:00:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 1.80/1.29 % SZS status Started for theBenchmark.p
% 1.80/1.29 % SZS status Theorem for theBenchmark.p
% 1.80/1.29
% 1.80/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.80/1.29
% 1.80/1.29 % ------ iProver source info
% 1.80/1.29
% 1.80/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.80/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.80/1.29 % git: non_committed_changes: false
% 1.80/1.29
% 1.80/1.29 % ------ Parsing...
% 1.80/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.80/1.29
% 1.80/1.29 % ------ 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 %
% 1.80/1.29
% 1.80/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.80/1.29
% 1.80/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.80/1.29 % ------ Proving...
% 1.80/1.29 % ------ Problem Properties
% 1.80/1.29
% 1.80/1.29 %
% 1.80/1.29 % clauses 17
% 1.80/1.29 % conjectures 2
% 1.80/1.29 % EPR 4
% 1.80/1.29 % Horn 14
% 1.80/1.29 % unary 9
% 1.80/1.29 % binary 2
% 1.80/1.29 % lits 32
% 1.80/1.29 % lits eq 20
% 1.80/1.29 % fd_pure 0
% 1.80/1.29 % fd_pseudo 0
% 1.80/1.29 % fd_cond 0
% 1.80/1.29 % fd_pseudo_cond 5
% 1.80/1.29 % AC symbols 0
% 1.80/1.29
% 1.80/1.29 % ------ Schedule dynamic 5 is on
% 1.80/1.29
% 1.80/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.80/1.29
% 1.80/1.29
% 1.80/1.29 % ------
% 1.80/1.29 % Current options:
% 1.80/1.29 % ------
% 1.80/1.29
% 1.80/1.29
% 1.80/1.29 %
% 1.80/1.29
% 1.80/1.29 % ------ Proving...
% 1.80/1.29 %
% 1.80/1.29
% 1.80/1.29 % SZS status Theorem for theBenchmark.p
% 1.80/1.29
% 1.80/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.80/1.30
% 1.80/1.30
%------------------------------------------------------------------------------