%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 02:57:29 PM UTC 2026
% Result : Theorem 0.68s 1.60s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 13 unt; 0 def)
% Number of atoms : 193 ( 77 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 77 ~; 89 |; 32 &)
% ( 5 <=>; 5 =>; 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 : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 86 !; 20 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ( k5_setfam_1(X0,X1) = k1_xboole_0
<=> ! [X2] :
( r2_hidden(X2,X1)
=> X2 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ( k5_setfam_1(X0,X1) = k1_xboole_0
<=> ! [X2] :
( r2_hidden(X2,X1)
=> X2 = k1_xboole_0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0] :
( X0 = k1_xboole_0
<=> ! [X1] : ~ r2_hidden(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = k3_tarski(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> ? [X3] :
( r2_hidden(X3,X0)
& r2_hidden(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f21,axiom,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> k5_setfam_1(X0,X1) = k3_tarski(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f35,plain,
? [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
& ( k5_setfam_1(X0,X1) = k1_xboole_0
<~> ! [X2] :
( ~ r2_hidden(X2,X1)
| X2 = k1_xboole_0 ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| k5_setfam_1(X0,X1) = k3_tarski(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,plain,
? [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
& ( k5_setfam_1(X0,X1) = k1_xboole_0
| ! [X2] :
( ~ r2_hidden(X2,X1)
| X2 = k1_xboole_0 ) )
& ( k5_setfam_1(X0,X1) != k1_xboole_0
| ? [X2] :
( r2_hidden(X2,X1)
& k1_xboole_0 != X2 ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f50,plain,
? [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
& ( k5_setfam_1(X0,X1) = k1_xboole_0
| ! [X2] :
( ~ r2_hidden(X2,X1)
| X2 = k1_xboole_0 ) )
& ( k5_setfam_1(X0,X1) != k1_xboole_0
| ? [X2] :
( r2_hidden(X2,X1)
& k1_xboole_0 != X2 ) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
? [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
& ( k5_setfam_1(X0,X1) = k1_xboole_0
| ! [X3] :
( ~ r2_hidden(X3,X1)
| k1_xboole_0 = X3 ) )
& ( k5_setfam_1(X0,X1) != k1_xboole_0
| ? [X2] :
( r2_hidden(X2,X1)
& k1_xboole_0 != X2 ) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
( m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0)))
& ( k1_xboole_0 = k5_setfam_1(sK0,sK1)
| ! [X3] :
( ~ r2_hidden(X3,sK1)
| k1_xboole_0 = X3 ) )
& ( k1_xboole_0 != k5_setfam_1(sK0,sK1)
| ( r2_hidden(sK2,sK1)
& k1_xboole_0 != sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f51]) ).
fof(f53,plain,
! [X0] :
( ( k1_xboole_0 != X0
| ! [X1] : ~ r2_hidden(X1,X0) )
& ( ? [X1] : r2_hidden(X1,X0)
| X0 = k1_xboole_0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0] :
( ( k1_xboole_0 != X0
| ! [X2] : ~ r2_hidden(X2,X0) )
& ( ? [X1] : r2_hidden(X1,X0)
| X0 = k1_xboole_0 ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ( k1_xboole_0 != X0
| ! [X2] : ~ r2_hidden(X2,X0) )
& ( r2_hidden(sK3(X0),X0)
| X0 = k1_xboole_0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f54]) ).
fof(f59,plain,
! [X0,X1] :
( ( k3_tarski(X0) != X1
| ! [X2] :
( ( ~ r2_hidden(X2,X1)
| ? [X3] :
( r2_hidden(X3,X0)
& r2_hidden(X2,X3) ) )
& ( ! [X3] :
( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X2,X3) )
| r2_hidden(X2,X1) ) ) )
& ( ? [X2] :
( ( r2_hidden(X2,X1)
| ? [X3] :
( r2_hidden(X3,X0)
& r2_hidden(X2,X3) ) )
& ( ~ r2_hidden(X2,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X2,X3) ) ) )
| X1 = k3_tarski(X0) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f60,plain,
! [X0,X1] :
( ( k3_tarski(X0) != X1
| ! [X5] :
( ( ~ r2_hidden(X5,X1)
| ? [X7] :
( r2_hidden(X7,X0)
& r2_hidden(X5,X7) ) )
& ( ! [X6] :
( ~ r2_hidden(X6,X0)
| ~ r2_hidden(X5,X6) )
| r2_hidden(X5,X1) ) ) )
& ( ? [X2] :
( ( r2_hidden(X2,X1)
| ? [X4] :
( r2_hidden(X4,X0)
& r2_hidden(X2,X4) ) )
& ( ~ r2_hidden(X2,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X2,X3) ) ) )
| X1 = k3_tarski(X0) ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ( k3_tarski(X0) != X1
| ! [X5] :
( ( ~ r2_hidden(X5,X1)
| ( r2_hidden(sK9(X0,X5),X0)
& r2_hidden(X5,sK9(X0,X5)) ) )
& ( ! [X6] :
( ~ r2_hidden(X6,X0)
| ~ r2_hidden(X5,X6) )
| r2_hidden(X5,X1) ) ) )
& ( ( ( r2_hidden(sK7(X0,X1),X1)
| ( r2_hidden(sK8(X0,X1),X0)
& r2_hidden(sK7(X0,X1),sK8(X0,X1)) ) )
& ( ~ r2_hidden(sK7(X0,X1),X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| ~ r2_hidden(sK7(X0,X1),X3) ) ) )
| X1 = k3_tarski(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f60]) ).
fof(f64,plain,
m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f52]) ).
fof(f65,plain,
! [X3] :
( k1_xboole_0 = k5_setfam_1(sK0,sK1)
| ~ r2_hidden(X3,sK1)
| k1_xboole_0 = X3 ),
inference(cnf_transformation,[],[f52]) ).
fof(f66,plain,
( k1_xboole_0 != k5_setfam_1(sK0,sK1)
| r2_hidden(sK2,sK1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f67,plain,
( k1_xboole_0 != k5_setfam_1(sK0,sK1)
| k1_xboole_0 != sK2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f70,plain,
! [X2,X0] :
( k1_xboole_0 != X0
| ~ r2_hidden(X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f71,plain,
! [X0] :
( r2_hidden(sK3(X0),X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f55]) ).
fof(f82,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| k5_setfam_1(X0,X1) = k3_tarski(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0,X1,X5] :
( k3_tarski(X0) != X1
| ~ r2_hidden(X5,X1)
| r2_hidden(sK9(X0,X5),X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f89,plain,
! [X0,X1,X6,X5] :
( k3_tarski(X0) != X1
| ~ r2_hidden(X6,X0)
| ~ r2_hidden(X5,X6)
| r2_hidden(X5,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f90,plain,
! [X0,X1] :
( r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK8(X0,X1),X0)
| k3_tarski(X0) = X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
! [X0,X1] :
( r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK7(X0,X1),sK8(X0,X1))
| k3_tarski(X0) = X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f95,plain,
! [X2] : ~ r2_hidden(X2,k1_xboole_0),
inference(equality_resolution,[],[f70]) ).
fof(f96,plain,
! [X0,X6,X5] :
( ~ r2_hidden(X6,X0)
| ~ r2_hidden(X5,X6)
| r2_hidden(X5,k3_tarski(X0)) ),
inference(equality_resolution,[],[f89]) ).
fof(f98,plain,
! [X0,X5] :
( ~ r2_hidden(X5,k3_tarski(X0))
| r2_hidden(sK9(X0,X5),X0) ),
inference(equality_resolution,[],[f87]) ).
tcf(c_49,negated_conjecture,
( ( k1_xboole_0 != sK2 )
| ( k5_setfam_1(sK0,sK1) != k1_xboole_0 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_50,negated_conjecture,
( r2_hidden(sK2,sK1)
| ( k5_setfam_1(sK0,sK1) != k1_xboole_0 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ( k5_setfam_1(sK0,sK1) = k1_xboole_0 )
| ~ r2_hidden(X0,sK1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f64]) ).
tcf(c_55,plain,
! [X0: $i] :
( r2_hidden(sK3(X0),X0)
| ( X0 = k1_xboole_0 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i] : ~ r2_hidden(X0,k1_xboole_0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( k5_setfam_1(X1,X0) = k3_tarski(X0) )
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK7(X0,X1),sK8(X0,X1))
| ( k3_tarski(X0) = X1 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK8(X0,X1),X0)
| r2_hidden(sK7(X0,X1),X1)
| ( k3_tarski(X0) = X1 ) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,k3_tarski(X2))
| ~ r2_hidden(X1,X2)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK9(X1,X0),X1)
| ~ r2_hidden(X0,k3_tarski(X1)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_950,plain,
! [X0: $i] : ~ r2_hidden(X0,k3_tarski(k1_xboole_0)),
inference(superposition,[status(thm)],[c_77,c_56]) ).
tcf(c_1012,plain,
k3_tarski(k1_xboole_0) = k1_xboole_0,
inference(superposition,[status(thm)],[c_55,c_950]) ).
tcf(c_1277,plain,
k5_setfam_1(sK0,sK1) = k3_tarski(sK1),
inference(superposition,[status(thm)],[c_52,c_67]) ).
tcf(c_1294,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ( k3_tarski(sK1) = k1_xboole_0 )
| ~ r2_hidden(X0,sK1) ),
inference(demodulation,[status(thm)],[c_51,c_1277]) ).
tcf(c_1295,plain,
( ( k1_xboole_0 != sK2 )
| ( k3_tarski(sK1) != k1_xboole_0 ) ),
inference(demodulation,[status(thm)],[c_49,c_1277]) ).
tcf(c_1296,plain,
( r2_hidden(sK2,sK1)
| ( k3_tarski(sK1) != k1_xboole_0 ) ),
inference(demodulation,[status(thm)],[c_50,c_1277]) ).
tcf(c_1339,plain,
! [X0: $i] :
( r2_hidden(sK7(k1_xboole_0,X0),X0)
| ( k3_tarski(k1_xboole_0) = X0 ) ),
inference(superposition,[status(thm)],[c_74,c_56]) ).
tcf(c_1355,plain,
! [X0: $i] :
( r2_hidden(sK7(k1_xboole_0,X0),X0)
| ( X0 = k1_xboole_0 ) ),
inference(light_normalisation,[status(thm)],[c_1339,c_1012]) ).
tcf(c_1496,plain,
! [X0: $i] :
( r2_hidden(sK7(sK1,X0),X0)
| ( k3_tarski(sK1) = k1_xboole_0 )
| ( k3_tarski(sK1) = X0 )
| ( sK8(sK1,X0) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_74,c_1294]) ).
tcf(c_2388,plain,
( ( k3_tarski(sK1) = k1_xboole_0 )
| ( sK8(sK1,k1_xboole_0) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_1496,c_56]) ).
tcf(c_3172,plain,
( r2_hidden(sK7(sK1,k1_xboole_0),k1_xboole_0)
| ( k3_tarski(sK1) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_2388,c_73]) ).
tcf(c_3174,plain,
k3_tarski(sK1) = k1_xboole_0,
inference(forward_subsumption_resolution,[status(thm)],[c_3172,c_56]) ).
tcf(c_3175,plain,
r2_hidden(sK2,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_1296,c_3174]) ).
tcf(c_3176,plain,
k1_xboole_0 != sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_1295,c_3174]) ).
tcf(c_3204,plain,
! [X0: $i] :
( r2_hidden(X0,k3_tarski(sK1))
| ~ r2_hidden(X0,sK2) ),
inference(superposition,[status(thm)],[c_3175,c_75]) ).
tcf(c_3218,plain,
! [X0: $i] :
( r2_hidden(X0,k1_xboole_0)
| ~ r2_hidden(X0,sK2) ),
inference(light_normalisation,[status(thm)],[c_3204,c_3174]) ).
tcf(c_3219,plain,
! [X0: $i] : ~ r2_hidden(X0,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_3218,c_56]) ).
tcf(c_3230,plain,
k1_xboole_0 = sK2,
inference(superposition,[status(thm)],[c_1355,c_3219]) ).
tcf(c_3231,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3230,c_3176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.78 % Computer : n026.cluster.edu
% 0.10/0.78 % Model : x86_64 x86_64
% 0.10/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.78 % Memory : 8046.5625MB
% 0.10/0.78 % OS : Linux 6.8.0-71-generic
% 0.10/0.78 % CPULimit : 300
% 0.10/0.78 % WCLimit : 300
% 0.10/0.78 % DateTime : Thu Sep 24 14:14:27 UTC 2026
% 0.10/0.78 % CPUTime :
% 0.10/0.78 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.82 Running first-order theorem proving
% 0.16/0.82 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
% 0.16/0.83
% 0.16/0.83 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.83
% 0.16/0.83 % Detected problem language: tptp
% 0.16/0.85 % Proving...
% 0.68/1.60 % SZS status Started for theBenchmark.p
% 0.68/1.60 % SZS status Theorem for theBenchmark.p
% 0.68/1.60
% 0.68/1.60 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.68/1.60
% 0.68/1.60 % ------ iProver source info
% 0.68/1.60
% 0.68/1.60 % git: date: 2026-07-19 20:42:38 +0200
% 0.68/1.60 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.68/1.60 % git: non_committed_changes: false
% 0.68/1.60
% 0.68/1.60 % ------ Parsing...
% 0.68/1.60 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.68/1.60
% 0.68/1.60 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.68/1.60
% 0.68/1.60 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.68/1.60
% 0.68/1.60 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.68/1.60 % ------ Proving...
% 0.68/1.60 % ------ Problem Properties
% 0.68/1.60
% 0.68/1.60 %
% 0.68/1.60 % clauses 31
% 0.68/1.60 % conjectures 4
% 0.68/1.60 % EPR 10
% 0.68/1.60 % Horn 25
% 0.68/1.60 % unary 9
% 0.68/1.60 % binary 13
% 0.68/1.60 % lits 63
% 0.68/1.60 % lits eq 12
% 0.68/1.60 % fd_pure 0
% 0.68/1.60 % fd_pseudo 0
% 0.68/1.60 % fd_cond 3
% 0.68/1.60 % fd_pseudo_cond 4
% 0.68/1.60 % AC symbols 0
% 0.68/1.60
% 0.68/1.60 % ------ Schedule dynamic 5 is on
% 0.68/1.60
% 0.68/1.60 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.68/1.60
% 0.68/1.60
% 0.68/1.60 % ------
% 0.68/1.60 % Current options:
% 0.68/1.60 % ------
% 0.68/1.60
% 0.68/1.60
% 0.68/1.60 %
% 0.68/1.60
% 0.68/1.60 % ------ Proving...
% 0.68/1.60 %
% 0.68/1.60
% 0.68/1.60 % SZS status Theorem for theBenchmark.p
% 0.68/1.60
% 0.68/1.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.68/1.60
% 0.68/1.60
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