%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 02:55:34 PM UTC 2026
% Result : Theorem 2.62s 1.18s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 17 unt; 2 def)
% Number of atoms : 207 ( 106 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 207 ( 77 ~; 92 |; 31 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% 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 : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn 89 !; 8 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
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,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f8,conjecture,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f9,negated_conjecture,
~ ! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
? [X0] : singleton(X0) != unordered_pair(X0,X0),
inference(ennf_transformation,[],[f9]) ).
fof(f13,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(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0,X1] :
( ( ( in(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) )
& ( ~ in(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f20]) ).
fof(f22,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f12]) ).
fof(f25,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f26]) ).
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,[],[f25]) ).
fof(f43,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f30]) ).
fof(f44,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_63,negated_conjecture,
unordered_pair(sK3,sK3) != singleton(sK3),
inference(cnf_transformation,[],[f37]) ).
tcf(c_206,definition,
iPr_def_10 = unordered_pair(sK3,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_207,definition,
iPr_def_11 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_208,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_63,c_207,c_206]) ).
tcf(c_416,plain,
in(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_207,c_53]) ).
tcf(c_417,plain,
in(sK3,iPr_def_10),
inference(superposition,[status(thm)],[c_206,c_59]) ).
tcf(c_437,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_207,c_54]) ).
tcf(c_450,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_206,c_60]) ).
tcf(c_502,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_11),X0)
| ( X0 = iPr_def_11 )
| ( sK2(X0,iPr_def_11) = sK3 ) ),
inference(superposition,[status(thm)],[c_62,c_437]) ).
tcf(c_550,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( sK2(iPr_def_10,iPr_def_11) = sK3 ) ),
inference(superposition,[status(thm)],[c_502,c_450]) ).
tcf(c_551,plain,
sK2(iPr_def_10,iPr_def_11) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_550,c_208]) ).
tcf(c_706,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ in(sK3,iPr_def_11)
| ~ in(sK2(iPr_def_10,iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_551,c_61]) ).
tcf(c_707,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ in(sK3,iPr_def_11)
| ~ in(sK3,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_706,c_551]) ).
tcf(c_708,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_707,c_208,c_416,c_417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.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 12:55:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.62/1.18 % SZS status Started for theBenchmark.p
% 2.62/1.18 % SZS status Theorem for theBenchmark.p
% 2.62/1.18
% 2.62/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.62/1.18
% 2.62/1.18 % ------ iProver source info
% 2.62/1.18
% 2.62/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.62/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.62/1.18 % git: non_committed_changes: false
% 2.62/1.18
% 2.62/1.18 % ------ Parsing...
% 2.62/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.62/1.18
% 2.62/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.62/1.18
% 2.62/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.62/1.18
% 2.62/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.62/1.18 % ------ Proving...
% 2.62/1.18 % ------ Problem Properties
% 2.62/1.18
% 2.62/1.18 %
% 2.62/1.18 % clauses 17
% 2.62/1.18 % conjectures 1
% 2.62/1.18 % EPR 2
% 2.62/1.18 % Horn 13
% 2.62/1.18 % unary 7
% 2.62/1.18 % binary 2
% 2.62/1.18 % lits 36
% 2.62/1.18 % lits eq 20
% 2.62/1.18 % fd_pure 0
% 2.62/1.18 % fd_pseudo 0
% 2.62/1.18 % fd_cond 0
% 2.62/1.18 % fd_pseudo_cond 7
% 2.62/1.18 % AC symbols 0
% 2.62/1.18
% 2.62/1.18 % ------ Schedule dynamic 5 is on
% 2.62/1.18
% 2.62/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.62/1.18
% 2.62/1.18
% 2.62/1.18 % ------
% 2.62/1.18 % Current options:
% 2.62/1.18 % ------
% 2.62/1.18
% 2.62/1.18
% 2.62/1.18 %
% 2.62/1.18
% 2.62/1.18 % ------ Proving...
% 2.62/1.18 %
% 2.62/1.18
% 2.62/1.18 % SZS status Theorem for theBenchmark.p
% 2.62/1.18
% 2.62/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.62/1.18
% 2.62/1.18
%------------------------------------------------------------------------------