%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU420+1 : TPTP v9.3.1. Released v3.4.0.
% 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 02:57:26 PM UTC 2026
% Result : Theorem 41.74s 6.78s
% Output : CNFRefutation 41.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 10 unt; 0 def)
% Number of atoms : 292 ( 29 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 370 ( 150 ~; 156 |; 49 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 188 ( 0 sgn 172 !; 16 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> r1_tarski(k9_relat_1(k3_xboole_0(X1,X2),k3_pua2mss1(X0)),k3_xboole_0(k9_relat_1(X1,k3_pua2mss1(X0)),k9_relat_1(X2,k3_pua2mss1(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> r1_tarski(k9_relat_1(k3_xboole_0(X1,X2),k3_pua2mss1(X0)),k3_xboole_0(k9_relat_1(X1,k3_pua2mss1(X0)),k9_relat_1(X2,k3_pua2mss1(X0)))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = k3_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f24,axiom,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_relat_1(X0) )
=> v1_relat_1(k3_xboole_0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f49,plain,
? [X0,X1] :
( v1_relat_1(X1)
& ? [X2] :
( v1_relat_1(X2)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(X1,X2),k3_pua2mss1(X0)),k3_xboole_0(k9_relat_1(X1,k3_pua2mss1(X0)),k9_relat_1(X2,k3_pua2mss1(X0)))) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| v1_relat_1(k3_xboole_0(X0,X1)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f56,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| v1_relat_1(k3_xboole_0(X0,X1)) ),
inference(flattening,[],[f55]) ).
fof(f67,plain,
( v1_relat_1(sK1)
& v1_relat_1(sK2)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
fof(f68,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( k9_relat_1(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) )
& ( ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,X3),X0) )
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) )
& ( ~ r2_hidden(X3,X2)
| ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,X3),X0) ) ) )
| X2 = k9_relat_1(X0,X1) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f69,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( k9_relat_1(X0,X1) != X2
| ! [X6] :
( ( ~ r2_hidden(X6,X2)
| ? [X8] :
( r2_hidden(X8,X1)
& r2_hidden(k4_tarski(X8,X6),X0) ) )
& ( ! [X7] :
( ~ r2_hidden(X7,X1)
| ~ r2_hidden(k4_tarski(X7,X6),X0) )
| r2_hidden(X6,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ? [X5] :
( r2_hidden(X5,X1)
& r2_hidden(k4_tarski(X5,X3),X0) ) )
& ( ~ r2_hidden(X3,X2)
| ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,X3),X0) ) ) )
| X2 = k9_relat_1(X0,X1) ) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( k9_relat_1(X0,X1) != X2
| ! [X6] :
( ( ~ r2_hidden(X6,X2)
| ( r2_hidden(sK5(X0,X1,X6),X1)
& r2_hidden(k4_tarski(sK5(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ r2_hidden(X7,X1)
| ~ r2_hidden(k4_tarski(X7,X6),X0) )
| r2_hidden(X6,X2) ) ) )
& ( ( ( r2_hidden(sK3(X0,X1,X2),X2)
| ( r2_hidden(sK4(X0,X1,X2),X1)
& r2_hidden(k4_tarski(sK4(X0,X1,X2),sK3(X0,X1,X2)),X0) ) )
& ( ~ r2_hidden(sK3(X0,X1,X2),X2)
| ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,sK3(X0,X1,X2)),X0) ) ) )
| X2 = k9_relat_1(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f72,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK6(X0,X1),X0)
& ~ r2_hidden(sK6(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X0) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X0) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ) ) )
& ( ( ( r2_hidden(sK7(X0,X1,X2),X2)
| ( r2_hidden(sK7(X0,X1,X2),X1)
& r2_hidden(sK7(X0,X1,X2),X0) ) )
& ( ~ r2_hidden(sK7(X0,X1,X2),X2)
| ~ r2_hidden(sK7(X0,X1,X2),X1)
| ~ r2_hidden(sK7(X0,X1,X2),X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f76]) ).
fof(f86,plain,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f87,plain,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f88,plain,
~ r1_tarski(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),
inference(cnf_transformation,[],[f67]) ).
fof(f93,plain,
! [X2,X0,X1,X6] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X6,X2)
| r2_hidden(sK5(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f94,plain,
! [X2,X0,X1,X6] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X6,X2)
| r2_hidden(k4_tarski(sK5(X0,X1,X6),X6),X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X2,X0,X1,X6,X7] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X7,X1)
| ~ r2_hidden(k4_tarski(X7,X6),X0)
| r2_hidden(X6,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X0,X1] :
( r2_hidden(sK6(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f101,plain,
! [X0,X1] :
( ~ r2_hidden(sK6(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f102,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f103,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f108,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f115,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| v1_relat_1(k3_xboole_0(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f144,plain,
! [X2,X0,X1,X6,X7] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X7,X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| r2_hidden(X6,X2) ),
inference(definition_unfolding,[],[f95,f108]) ).
fof(f145,plain,
! [X2,X0,X1,X6] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X6,X2)
| r2_hidden(k2_tarski(k2_tarski(sK5(X0,X1,X6),X6),k1_tarski(sK5(X0,X1,X6))),X0) ),
inference(definition_unfolding,[],[f94,f108]) ).
fof(f146,plain,
! [X0,X1,X6,X7] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(X7,X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| r2_hidden(X6,k9_relat_1(X0,X1)) ),
inference(equality_resolution,[],[f144]) ).
fof(f147,plain,
! [X0,X1,X6] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(X6,k9_relat_1(X0,X1))
| r2_hidden(k2_tarski(k2_tarski(sK5(X0,X1,X6),X6),k1_tarski(sK5(X0,X1,X6))),X0) ),
inference(equality_resolution,[],[f145]) ).
fof(f148,plain,
! [X0,X1,X6] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(X6,k9_relat_1(X0,X1))
| r2_hidden(sK5(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f93]) ).
fof(f149,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,k3_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f104]) ).
fof(f150,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f103]) ).
fof(f151,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X1) ),
inference(equality_resolution,[],[f102]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),
inference(cnf_transformation,[],[f88]) ).
tcf(c_50,negated_conjecture,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f87]) ).
tcf(c_51,negated_conjecture,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f86]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X1,k9_relat_1(X2,X3))
| ~ v1_relat_1(X2)
| ~ r2_hidden(X0,X3)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k2_tarski(sK5(X1,X2,X0),X0),k1_tarski(sK5(X1,X2,X0))),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(sK5(X1,X2,X0),X2)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,X2)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,k3_xboole_0(X2,X1))
| ~ r2_hidden(X0,X2)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X1)
| ~ r2_hidden(X0,k3_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X2)
| ~ r2_hidden(X0,k3_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(k3_xboole_0(X1,X0))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK6(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_160]) ).
tcf(c_779,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK6(X1,X0),X1)
| ( k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)) != X1 )
| ( k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_161]) ).
tcf(c_780,plain,
r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0))),
inference(unflattening,[status(thm)],[c_779]) ).
tcf(c_2442,plain,
( r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),k3_xboole_0(sK1,sK2))
| ~ v1_relat_1(k3_xboole_0(sK1,sK2))
| ~ r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_2443,plain,
( r2_hidden(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k3_pua2mss1(sK0))
| ~ v1_relat_1(k3_xboole_0(sK1,sK2))
| ~ r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0))) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2565,plain,
( v1_relat_1(k3_xboole_0(sK1,sK2))
| ~ v1_relat_1(sK2)
| ~ v1_relat_1(sK1) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_2923,plain,
( r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),sK2)
| ~ r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),k3_xboole_0(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2924,plain,
( r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),sK1)
| ~ r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),k3_xboole_0(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_3481,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_tarski(X0,k3_xboole_0(X1,X2))
| ~ r2_hidden(sK6(X0,k3_xboole_0(X1,X2)),X2)
| ~ r2_hidden(sK6(X0,k3_xboole_0(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_68,c_62]) ).
tcf(c_7341,plain,
( r1_tarski(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))
| ~ r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(sK2,k3_pua2mss1(sK0)))
| ~ r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(sK1,k3_pua2mss1(sK0))) ),
inference(instantiation,[status(thm)],[c_3481]) ).
tcf(c_8483,plain,
! [X0: $i] :
( r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(sK2,X0))
| ~ v1_relat_1(sK2)
| ~ r2_hidden(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),sK2) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_8495,plain,
! [X0: $i] :
( r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(sK1,X0))
| ~ v1_relat_1(sK1)
| ~ r2_hidden(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),sK1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_14502,plain,
( r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(sK2,k3_pua2mss1(sK0)))
| ~ v1_relat_1(sK2)
| ~ r2_hidden(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k3_pua2mss1(sK0))
| ~ r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),sK2) ),
inference(instantiation,[status(thm)],[c_8483]) ).
tcf(c_14656,plain,
( r2_hidden(sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0)))),k9_relat_1(sK1,k3_pua2mss1(sK0)))
| ~ v1_relat_1(sK1)
| ~ r2_hidden(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k3_pua2mss1(sK0))
| ~ r2_hidden(k2_tarski(k2_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))),k1_tarski(sK5(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0),sK6(k9_relat_1(k3_xboole_0(sK1,sK2),k3_pua2mss1(sK0)),k3_xboole_0(k9_relat_1(sK1,k3_pua2mss1(sK0)),k9_relat_1(sK2,k3_pua2mss1(sK0))))))),sK1) ),
inference(instantiation,[status(thm)],[c_8495]) ).
tcf(c_14657,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14656,c_14502,c_7341,c_2923,c_2924,c_2565,c_2442,c_2443,c_780,c_49,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU420+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 14:07:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 41.74/6.78 % SZS status Started for theBenchmark.p
% 41.74/6.78 % SZS status Theorem for theBenchmark.p
% 41.74/6.78
% 41.74/6.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 41.74/6.78
% 41.74/6.78 % ------ iProver source info
% 41.74/6.78
% 41.74/6.78 % git: date: 2026-07-19 20:42:38 +0200
% 41.74/6.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 41.74/6.78 % git: non_committed_changes: false
% 41.74/6.78
% 41.74/6.78 % ------ Parsing...
% 41.74/6.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 41.74/6.78
% 41.74/6.78 % ------ 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 %
% 41.74/6.78
% 41.74/6.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 41.74/6.78
% 41.74/6.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 41.74/6.78 % ------ Proving...
% 41.74/6.78 % ------ Problem Properties
% 41.74/6.78
% 41.74/6.78 %
% 41.74/6.78 % clauses 52
% 41.74/6.78 % conjectures 3
% 41.74/6.78 % EPR 20
% 41.74/6.78 % Horn 45
% 41.74/6.78 % unary 23
% 41.74/6.78 % binary 13
% 41.74/6.78 % lits 103
% 41.74/6.78 % lits eq 12
% 41.74/6.78 % fd_pure 0
% 41.74/6.78 % fd_pseudo 0
% 41.74/6.78 % fd_cond 1
% 41.74/6.78 % fd_pseudo_cond 7
% 41.74/6.78 % AC symbols 0
% 41.74/6.78
% 41.74/6.78 % ------ Input Options Time Limit: Unbounded
% 41.74/6.78
% 41.74/6.78
% 41.74/6.78 % ------
% 41.74/6.78 % Current options:
% 41.74/6.78 % ------
% 41.74/6.78
% 41.74/6.78
% 41.74/6.78 %
% 41.74/6.78
% 41.74/6.78 % ------ Proving...
% 41.74/6.78 %
% 41.74/6.78
% 41.74/6.78 % SZS status Theorem for theBenchmark.p
% 41.74/6.78
% 41.74/6.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 41.74/6.79
% 41.74/6.79
%------------------------------------------------------------------------------