TSTP Solution File: SEU406+3 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU406+3 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:19:44 EDT 2022
% Result : Theorem 1.24s 5.42s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 31
% Syntax : Number of formulae : 186 ( 132 unt; 0 def)
% Number of atoms : 299 ( 140 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 206 ( 93 ~; 69 |; 36 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 311 ( 36 sgn 149 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t1_latsum_1,conjecture,
! [X1,X2,X3,X4] :
~ ( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,k4_xboole_0(X3,X4)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_latsum_1) ).
fof(t68_zfmisc_1,axiom,
! [X1,X2] :
( k4_xboole_0(k1_tarski(X1),X2) = k1_xboole_0
<=> r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t68_zfmisc_1) ).
fof(t6_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k2_xboole_0(X1,X2)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t6_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(t39_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t39_xboole_1) ).
fof(t4_xboole_1,axiom,
! [X1,X2,X3] : k2_xboole_0(k2_xboole_0(X1,X2),X3) = k2_xboole_0(X1,k2_xboole_0(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t4_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : k2_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t1_boole) ).
fof(t40_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(k2_xboole_0(X1,X2),X2) = k4_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t40_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : r1_tarski(X1,k2_xboole_0(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t7_xboole_1) ).
fof(t5_xboole_0,axiom,
! [X1,X2,X3] :
~ ( r1_xboole_0(X1,X2)
& r2_hidden(X3,k2_xboole_0(X1,X2))
& ~ ( r2_hidden(X3,X1)
& ~ r2_hidden(X3,X2) )
& ~ ( r2_hidden(X3,X2)
& ~ r2_hidden(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',t5_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',idempotence_k2_xboole_0) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( k4_xboole_0(X1,X2) = k1_xboole_0
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t37_xboole_1) ).
fof(t83_xboole_1,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
<=> k4_xboole_0(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t83_xboole_1) ).
fof(t47_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k3_xboole_0(X1,X2)) = k4_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t47_xboole_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t48_xboole_1) ).
fof(t52_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k3_xboole_0(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t52_xboole_1) ).
fof(t54_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k3_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t54_xboole_1) ).
fof(t79_xboole_1,axiom,
! [X1,X2] : r1_xboole_0(k4_xboole_0(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t79_xboole_1) ).
fof(t41_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(k4_xboole_0(X1,X2),X3) = k4_xboole_0(X1,k2_xboole_0(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t41_xboole_1) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
=> k2_xboole_0(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t12_xboole_1) ).
fof(t36_xboole_1,axiom,
! [X1,X2] : r1_tarski(k4_xboole_0(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t36_xboole_1) ).
fof(t55_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(k2_xboole_0(X1,X2),k3_xboole_0(X1,X2)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t55_xboole_1) ).
fof(t49_xboole_1,axiom,
! [X1,X2,X3] : k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t49_xboole_1) ).
fof(t53_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k2_xboole_0(X2,X3)) = k3_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t53_xboole_1) ).
fof(t38_xboole_1,axiom,
! [X1,X2] :
( r1_tarski(X1,k4_xboole_0(X2,X1))
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t38_xboole_1) ).
fof(t65_zfmisc_1,axiom,
! [X1,X2] :
( k4_xboole_0(X1,k1_tarski(X2)) = X1
<=> ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t65_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t3_boole) ).
fof(t81_xboole_1,axiom,
! [X1,X2,X3] :
( r1_xboole_0(X1,k4_xboole_0(X2,X3))
=> r1_xboole_0(X2,k4_xboole_0(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t81_xboole_1) ).
fof(t67_zfmisc_1,axiom,
! [X1,X2] :
( k4_xboole_0(k1_tarski(X1),X2) = k1_tarski(X1)
<=> ~ r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t67_zfmisc_1) ).
fof(t111_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(k3_xboole_0(X1,X2),k3_xboole_0(X3,X2)) = k3_xboole_0(k4_xboole_0(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t111_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : k4_xboole_0(k1_xboole_0,X1) = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t4_boole) ).
fof(c_0_31,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,k4_xboole_0(X3,X4)) ) ),
inference(assume_negation,[status(cth)],[t1_latsum_1]) ).
fof(c_0_32,plain,
! [X3,X4,X3,X4] :
( ( k4_xboole_0(k1_tarski(X3),X4) != k1_xboole_0
| r2_hidden(X3,X4) )
& ( ~ r2_hidden(X3,X4)
| k4_xboole_0(k1_tarski(X3),X4) = k1_xboole_0 ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_zfmisc_1])])])]) ).
fof(c_0_33,negated_conjecture,
( r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0))
& r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0))
& ( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) )
& ( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0) )
& ( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,esk4_0) )
& ( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
fof(c_0_34,plain,
! [X3,X4] : k2_xboole_0(X3,k2_xboole_0(X3,X4)) = k2_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t6_xboole_1]) ).
fof(c_0_35,plain,
! [X3,X4] : k2_xboole_0(X3,X4) = k2_xboole_0(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_36,plain,
! [X3,X4] : k2_xboole_0(X3,k4_xboole_0(X4,X3)) = k2_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_37,plain,
( k4_xboole_0(k1_tarski(X1),X2) = k1_xboole_0
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X4,X5,X6] : k2_xboole_0(k2_xboole_0(X4,X5),X6) = k2_xboole_0(X4,k2_xboole_0(X5,X6)),
inference(variable_rename,[status(thm)],[t4_xboole_1]) ).
fof(c_0_40,plain,
! [X2] : k2_xboole_0(X2,k1_xboole_0) = X2,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(c_0_41,plain,
! [X3,X4] : k4_xboole_0(k2_xboole_0(X3,X4),X4) = k4_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_42,plain,
k2_xboole_0(X1,k2_xboole_0(X1,X2)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,negated_conjecture,
k4_xboole_0(k1_tarski(esk1_0),k2_xboole_0(esk3_0,esk4_0)) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
k2_xboole_0(k2_xboole_0(X1,X2),X3) = k2_xboole_0(X1,k2_xboole_0(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
k2_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
k4_xboole_0(k2_xboole_0(X1,X2),X2) = k4_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
k2_xboole_0(X1,k2_xboole_0(X2,X1)) = k2_xboole_0(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
k2_xboole_0(esk3_0,k2_xboole_0(esk4_0,k1_tarski(esk1_0))) = k2_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]),c_0_46]) ).
cnf(c_0_51,plain,
k2_xboole_0(X1,k2_xboole_0(X2,X3)) = k2_xboole_0(X3,k2_xboole_0(X1,X2)),
inference(spm,[status(thm)],[c_0_43,c_0_46]) ).
fof(c_0_52,plain,
! [X3,X4] : r1_tarski(X3,k2_xboole_0(X3,X4)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_53,plain,
k4_xboole_0(k2_xboole_0(X1,X2),X1) = k4_xboole_0(X2,X1),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
cnf(c_0_54,negated_conjecture,
k2_xboole_0(esk4_0,k2_xboole_0(esk3_0,k1_tarski(esk1_0))) = k2_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_46]),c_0_51]),c_0_43]),c_0_42]) ).
fof(c_0_55,plain,
! [X4,X5,X6] :
( ( r2_hidden(X6,X5)
| r2_hidden(X6,X4)
| ~ r1_xboole_0(X4,X5)
| ~ r2_hidden(X6,k2_xboole_0(X4,X5)) )
& ( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X4)
| ~ r1_xboole_0(X4,X5)
| ~ r2_hidden(X6,k2_xboole_0(X4,X5)) )
& ( r2_hidden(X6,X5)
| ~ r2_hidden(X6,X5)
| ~ r1_xboole_0(X4,X5)
| ~ r2_hidden(X6,k2_xboole_0(X4,X5)) )
& ( ~ r2_hidden(X6,X4)
| ~ r2_hidden(X6,X5)
| ~ r1_xboole_0(X4,X5)
| ~ r2_hidden(X6,k2_xboole_0(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t5_xboole_0])])])]) ).
fof(c_0_56,plain,
! [X3] : k2_xboole_0(X3,X3) = X3,
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(c_0_57,plain,
! [X3,X4,X3,X4] :
( ( k4_xboole_0(X3,X4) != k1_xboole_0
| r1_tarski(X3,X4) )
& ( ~ r1_tarski(X3,X4)
| k4_xboole_0(X3,X4) = k1_xboole_0 ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])])]) ).
cnf(c_0_58,plain,
r1_tarski(X1,k2_xboole_0(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k4_xboole_0(X2,X1)) = k4_xboole_0(X1,k4_xboole_0(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_60,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk3_0,k1_tarski(esk1_0)),esk4_0) = k4_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48]) ).
cnf(c_0_61,plain,
( ~ r2_hidden(X1,k2_xboole_0(X2,X3))
| ~ r1_xboole_0(X2,X3)
| ~ r2_hidden(X1,X3)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
k2_xboole_0(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_63,plain,
! [X3,X4,X3,X4] :
( ( ~ r1_xboole_0(X3,X4)
| k4_xboole_0(X3,X4) = X3 )
& ( k4_xboole_0(X3,X4) != X3
| r1_xboole_0(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])])])]) ).
cnf(c_0_64,plain,
( k4_xboole_0(X1,X2) = k1_xboole_0
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
r1_tarski(X1,X1),
inference(spm,[status(thm)],[c_0_58,c_0_47]) ).
fof(c_0_66,plain,
! [X3,X4] : k4_xboole_0(X3,k3_xboole_0(X3,X4)) = k4_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t47_xboole_1]) ).
fof(c_0_67,plain,
! [X3,X4] : k4_xboole_0(X3,k4_xboole_0(X3,X4)) = k3_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_68,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk3_0,esk4_0),k4_xboole_0(esk3_0,esk4_0)) = k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_54]) ).
fof(c_0_69,plain,
! [X4,X5,X6] : k4_xboole_0(X4,k4_xboole_0(X5,X6)) = k2_xboole_0(k4_xboole_0(X4,X5),k3_xboole_0(X4,X6)),
inference(variable_rename,[status(thm)],[t52_xboole_1]) ).
fof(c_0_70,plain,
! [X4,X5,X6] : k4_xboole_0(X4,k3_xboole_0(X5,X6)) = k2_xboole_0(k4_xboole_0(X4,X5),k4_xboole_0(X4,X6)),
inference(variable_rename,[status(thm)],[t54_xboole_1]) ).
fof(c_0_71,plain,
! [X3,X4] : r1_xboole_0(k4_xboole_0(X3,X4),X4),
inference(variable_rename,[status(thm)],[t79_xboole_1]) ).
fof(c_0_72,plain,
! [X4,X5,X6] : k4_xboole_0(k4_xboole_0(X4,X5),X6) = k4_xboole_0(X4,k2_xboole_0(X5,X6)),
inference(variable_rename,[status(thm)],[t41_xboole_1]) ).
fof(c_0_73,plain,
! [X3,X4] :
( ~ r1_tarski(X3,X4)
| k2_xboole_0(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_74,plain,
! [X3,X4] : r1_tarski(k4_xboole_0(X3,X4),X3),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_75,plain,
( ~ r1_xboole_0(X1,X1)
| ~ r2_hidden(X2,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_76,plain,
( r1_xboole_0(X1,X2)
| k4_xboole_0(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_77,plain,
k4_xboole_0(X1,X1) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_78,plain,
( r2_hidden(X1,X2)
| k4_xboole_0(k1_tarski(X1),X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_79,plain,
! [X3,X4] : k4_xboole_0(k2_xboole_0(X3,X4),k3_xboole_0(X3,X4)) = k2_xboole_0(k4_xboole_0(X3,X4),k4_xboole_0(X4,X3)),
inference(variable_rename,[status(thm)],[t55_xboole_1]) ).
cnf(c_0_80,plain,
k4_xboole_0(X1,k3_xboole_0(X1,X2)) = k4_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_81,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_82,negated_conjecture,
k2_xboole_0(esk4_0,k2_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))) = k2_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_68]),c_0_44]),c_0_51]),c_0_43]),c_0_43]),c_0_44]),c_0_43]) ).
fof(c_0_83,plain,
! [X4,X5,X6] : k3_xboole_0(X4,k4_xboole_0(X5,X6)) = k4_xboole_0(k3_xboole_0(X4,X5),X6),
inference(variable_rename,[status(thm)],[t49_xboole_1]) ).
fof(c_0_84,plain,
! [X4,X5,X6] : k4_xboole_0(X4,k2_xboole_0(X5,X6)) = k3_xboole_0(k4_xboole_0(X4,X5),k4_xboole_0(X4,X6)),
inference(variable_rename,[status(thm)],[t53_xboole_1]) ).
cnf(c_0_85,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k3_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_86,plain,
k4_xboole_0(X1,k3_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_87,plain,
r1_xboole_0(k4_xboole_0(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_88,plain,
k4_xboole_0(k4_xboole_0(X1,X2),X3) = k4_xboole_0(X1,k2_xboole_0(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_89,plain,
( k2_xboole_0(X1,X2) = X2
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_90,plain,
r1_tarski(k4_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_91,plain,
! [X3,X4] :
( ~ r1_tarski(X3,k4_xboole_0(X4,X3))
| X3 = k1_xboole_0 ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_xboole_1])])])]) ).
fof(c_0_92,plain,
! [X3,X4,X3,X4] :
( ( k4_xboole_0(X3,k1_tarski(X4)) != X3
| ~ r2_hidden(X4,X3) )
& ( r2_hidden(X4,X3)
| k4_xboole_0(X3,k1_tarski(X4)) = X3 ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t65_zfmisc_1])])])])]) ).
cnf(c_0_93,plain,
( k1_xboole_0 != X1
| ~ r2_hidden(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_94,plain,
r2_hidden(X1,k1_tarski(X1)),
inference(spm,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_95,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_96,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k3_xboole_0(X1,X2)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_97,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X1,X2))) = k4_xboole_0(X1,X2),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_98,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)),esk4_0) = k4_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_82]),c_0_48]) ).
cnf(c_0_99,plain,
k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_100,plain,
k4_xboole_0(X1,k2_xboole_0(X2,X3)) = k3_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_101,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,k4_xboole_0(X1,X3))),
inference(rw,[status(thm)],[c_0_85,c_0_81]) ).
cnf(c_0_102,plain,
k4_xboole_0(X1,k4_xboole_0(X2,k4_xboole_0(X2,X3))) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
inference(rw,[status(thm)],[c_0_86,c_0_81]) ).
fof(c_0_103,plain,
! [X2] : k4_xboole_0(X2,k1_xboole_0) = X2,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_104,plain,
! [X4,X5,X6] :
( ~ r1_xboole_0(X4,k4_xboole_0(X5,X6))
| r1_xboole_0(X5,k4_xboole_0(X4,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t81_xboole_1])]) ).
cnf(c_0_105,plain,
r1_xboole_0(k4_xboole_0(X1,k2_xboole_0(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_106,plain,
k2_xboole_0(X1,k4_xboole_0(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_43]) ).
cnf(c_0_107,plain,
( X1 = k1_xboole_0
| ~ r1_tarski(X1,k4_xboole_0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_108,plain,
( k4_xboole_0(X1,k1_tarski(X2)) = X1
| r2_hidden(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_109,plain,
k1_tarski(X1) != k1_xboole_0,
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_110,plain,
k2_xboole_0(X1,k4_xboole_0(X2,k2_xboole_0(X3,X1))) = k2_xboole_0(X1,k4_xboole_0(X2,X3)),
inference(spm,[status(thm)],[c_0_44,c_0_88]) ).
cnf(c_0_111,negated_conjecture,
k4_xboole_0(k1_tarski(esk2_0),k2_xboole_0(esk3_0,esk4_0)) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_37,c_0_95]) ).
fof(c_0_112,plain,
! [X3,X4,X3,X4] :
( ( k4_xboole_0(k1_tarski(X3),X4) != k1_tarski(X3)
| ~ r2_hidden(X3,X4) )
& ( r2_hidden(X3,X4)
| k4_xboole_0(k1_tarski(X3),X4) = k1_tarski(X3) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t67_zfmisc_1])])])])]) ).
cnf(c_0_113,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k4_xboole_0(X1,k4_xboole_0(X1,X2))) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X2,X1)),
inference(rw,[status(thm)],[c_0_96,c_0_81]) ).
cnf(c_0_114,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)),k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))) = k4_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_48]) ).
cnf(c_0_115,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X2,X3))) = k4_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_81]),c_0_81]) ).
cnf(c_0_116,plain,
k4_xboole_0(X1,k2_xboole_0(X2,X3)) = k4_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3))),
inference(rw,[status(thm)],[c_0_100,c_0_81]) ).
cnf(c_0_117,plain,
k4_xboole_0(X1,k4_xboole_0(X2,k4_xboole_0(X2,k4_xboole_0(X1,X3)))) = k4_xboole_0(X1,k4_xboole_0(X2,X3)),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_118,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_119,plain,
( r1_xboole_0(X1,k4_xboole_0(X2,X3))
| ~ r1_xboole_0(X2,k4_xboole_0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_120,plain,
r1_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X2,X3)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_121,plain,
( r2_hidden(X1,X2)
| ~ r1_tarski(k1_tarski(X1),X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_122,plain,
r1_tarski(X1,k2_xboole_0(X2,X1)),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_123,negated_conjecture,
k2_xboole_0(esk4_0,k4_xboole_0(k1_tarski(esk2_0),esk3_0)) = esk4_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_47]) ).
cnf(c_0_124,plain,
( k4_xboole_0(k1_tarski(X1),X2) = k1_tarski(X1)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_125,negated_conjecture,
k4_xboole_0(esk3_0,k4_xboole_0(esk4_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]),c_0_116]),c_0_102]),c_0_117]),c_0_117]),c_0_46]),c_0_102]),c_0_117]),c_0_77]),c_0_118]),c_0_62]),c_0_48]),c_0_97]) ).
cnf(c_0_126,plain,
( k4_xboole_0(X1,X2) = X1
| ~ r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_127,plain,
r1_xboole_0(X1,k4_xboole_0(k4_xboole_0(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
fof(c_0_128,plain,
! [X4,X5,X6] : k4_xboole_0(k3_xboole_0(X4,X5),k3_xboole_0(X6,X5)) = k3_xboole_0(k4_xboole_0(X4,X6),X5),
inference(variable_rename,[status(thm)],[t111_xboole_1]) ).
cnf(c_0_129,plain,
r2_hidden(X1,k2_xboole_0(X2,k1_tarski(X1))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( k2_xboole_0(esk4_0,k1_tarski(esk2_0)) = esk4_0
| r2_hidden(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,negated_conjecture,
k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))),
inference(spm,[status(thm)],[c_0_117,c_0_125]) ).
cnf(c_0_132,plain,
k4_xboole_0(X1,k4_xboole_0(k4_xboole_0(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,plain,
k4_xboole_0(k3_xboole_0(X1,X2),k3_xboole_0(X3,X2)) = k3_xboole_0(k4_xboole_0(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_134,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_135,negated_conjecture,
( r2_hidden(esk2_0,esk3_0)
| r2_hidden(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_77]),c_0_118]),c_0_77]),c_0_118]) ).
cnf(c_0_137,negated_conjecture,
k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))) = k4_xboole_0(esk4_0,esk3_0),
inference(rw,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_138,plain,
k4_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),k4_xboole_0(X3,k4_xboole_0(X3,X2))) = k4_xboole_0(k4_xboole_0(X1,X3),k4_xboole_0(k4_xboole_0(X1,X3),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_81]),c_0_81]),c_0_81]) ).
cnf(c_0_139,negated_conjecture,
( r2_hidden(esk2_0,esk3_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
fof(c_0_140,plain,
! [X2] : k4_xboole_0(k1_xboole_0,X2) = k1_xboole_0,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_141,plain,
( ~ r2_hidden(X1,X2)
| k4_xboole_0(k1_tarski(X1),X2) != k1_tarski(X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_142,negated_conjecture,
k2_xboole_0(k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))),k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0)))) = k2_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_131]),c_0_43]),c_0_43]) ).
cnf(c_0_143,negated_conjecture,
k4_xboole_0(k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0))),k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0))),
inference(spm,[status(thm)],[c_0_136,c_0_131]) ).
cnf(c_0_144,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))),k4_xboole_0(esk4_0,k4_xboole_0(esk4_0,esk3_0))) = k4_xboole_0(esk4_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_137]),c_0_115]),c_0_77]),c_0_118]),c_0_77]),c_0_47]) ).
cnf(c_0_145,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X2,k4_xboole_0(X3,k4_xboole_0(X3,X2))))) = k4_xboole_0(k4_xboole_0(X1,X3),k4_xboole_0(k4_xboole_0(X1,X3),X2)),
inference(rw,[status(thm)],[c_0_138,c_0_115]) ).
cnf(c_0_146,plain,
k2_xboole_0(X1,k2_xboole_0(X2,X3)) = k2_xboole_0(X2,k2_xboole_0(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_46]) ).
cnf(c_0_147,plain,
( k4_xboole_0(k4_xboole_0(k1_tarski(X1),X2),X3) = k1_tarski(X1)
| r2_hidden(X1,k2_xboole_0(X2,X3)) ),
inference(spm,[status(thm)],[c_0_124,c_0_88]) ).
cnf(c_0_148,negated_conjecture,
( k4_xboole_0(k1_tarski(esk2_0),esk3_0) = k1_xboole_0
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_139]) ).
cnf(c_0_149,plain,
k4_xboole_0(k1_xboole_0,X1) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_150,negated_conjecture,
k1_tarski(esk2_0) != k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_111]),c_0_95])]) ).
cnf(c_0_151,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0)))),k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_142]),c_0_143]) ).
cnf(c_0_152,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k4_xboole_0(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_59,c_0_136]) ).
cnf(c_0_153,negated_conjecture,
k2_xboole_0(esk4_0,k2_xboole_0(k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)),k4_xboole_0(esk4_0,k4_xboole_0(esk4_0,esk3_0)))) = esk4_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_144]),c_0_102]),c_0_145]),c_0_77]),c_0_118]),c_0_77]),c_0_118]),c_0_77]),c_0_118]),c_0_146]),c_0_43]) ).
cnf(c_0_154,plain,
( r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X2,X3))
| ~ r1_xboole_0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_155,plain,
r1_xboole_0(X1,k4_xboole_0(X2,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_136]) ).
cnf(c_0_156,negated_conjecture,
( r2_hidden(esk2_0,k2_xboole_0(esk3_0,X1))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_150]) ).
cnf(c_0_157,plain,
k2_xboole_0(X1,k2_xboole_0(X2,k4_xboole_0(X1,X3))) = k2_xboole_0(X2,X1),
inference(spm,[status(thm)],[c_0_146,c_0_106]) ).
cnf(c_0_158,negated_conjecture,
k4_xboole_0(esk4_0,k4_xboole_0(k2_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0)))),k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk4_0,k4_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_151]),c_0_48]),c_0_131]) ).
cnf(c_0_159,negated_conjecture,
k4_xboole_0(k2_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))),k4_xboole_0(esk4_0,esk3_0)) = k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_137]),c_0_43]) ).
cnf(c_0_160,negated_conjecture,
k2_xboole_0(esk4_0,k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))) = esk4_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_153]),c_0_46]),c_0_43]),c_0_106]),c_0_43]) ).
cnf(c_0_161,negated_conjecture,
k2_xboole_0(esk4_0,k4_xboole_0(k1_tarski(esk1_0),esk3_0)) = esk4_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_45]),c_0_47]) ).
cnf(c_0_162,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_44]),c_0_155])]) ).
cnf(c_0_163,negated_conjecture,
( r2_hidden(esk2_0,k2_xboole_0(X1,esk3_0))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_164,negated_conjecture,
k4_xboole_0(esk4_0,k4_xboole_0(k2_xboole_0(esk3_0,esk4_0),k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk4_0,k4_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_132]),c_0_43]),c_0_137]) ).
cnf(c_0_165,negated_conjecture,
k4_xboole_0(esk4_0,k4_xboole_0(esk4_0,esk3_0)) = k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_166,negated_conjecture,
( k2_xboole_0(esk4_0,k1_tarski(esk1_0)) = esk4_0
| r2_hidden(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_161,c_0_124]) ).
cnf(c_0_167,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_168,negated_conjecture,
( r2_hidden(esk2_0,k4_xboole_0(esk3_0,X1))
| r2_hidden(esk2_0,X1)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_169,negated_conjecture,
k4_xboole_0(esk4_0,k4_xboole_0(k2_xboole_0(esk3_0,esk4_0),k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))) = k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( r2_hidden(esk1_0,esk3_0)
| r2_hidden(esk1_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_129,c_0_166]) ).
cnf(c_0_171,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_134]) ).
cnf(c_0_172,negated_conjecture,
k2_xboole_0(esk4_0,k4_xboole_0(k2_xboole_0(esk3_0,esk4_0),k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0)))) = k2_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_169]),c_0_43]),c_0_44]),c_0_146]),c_0_43]),c_0_160]),c_0_43]) ).
cnf(c_0_173,negated_conjecture,
r2_hidden(esk1_0,esk3_0),
inference(sr,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_174,negated_conjecture,
k4_xboole_0(k4_xboole_0(k2_xboole_0(esk3_0,esk4_0),k4_xboole_0(esk3_0,k4_xboole_0(esk3_0,esk4_0))),esk4_0) = k4_xboole_0(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_172]),c_0_48]) ).
cnf(c_0_175,negated_conjecture,
k4_xboole_0(k1_tarski(esk1_0),esk3_0) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_37,c_0_173]) ).
cnf(c_0_176,negated_conjecture,
k1_tarski(esk1_0) != k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_45]),c_0_38])]) ).
cnf(c_0_177,negated_conjecture,
( r2_hidden(X1,k4_xboole_0(esk3_0,esk4_0))
| r2_hidden(X1,esk4_0)
| ~ r2_hidden(X1,k2_xboole_0(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_172]),c_0_174]) ).
cnf(c_0_178,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,X1)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_175]),c_0_149]),c_0_176]) ).
cnf(c_0_179,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_180,negated_conjecture,
r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_171]) ).
cnf(c_0_181,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_182,negated_conjecture,
( r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| r2_hidden(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_95]) ).
cnf(c_0_183,negated_conjecture,
~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_180])]) ).
cnf(c_0_184,negated_conjecture,
~ r2_hidden(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_180])]) ).
cnf(c_0_185,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_182,c_0_183]),c_0_184]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEU406+3 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.11 % Command : run_ET %s %d
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Sun Jun 19 02:59:34 EDT 2022
% 0.11/0.31 % CPUTime :
% 1.24/5.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 1.24/5.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 1.24/5.42 # Preprocessing time : 0.674 s
% 1.24/5.42
% 1.24/5.42 # Proof found!
% 1.24/5.42 # SZS status Theorem
% 1.24/5.42 # SZS output start CNFRefutation
% See solution above
% 1.24/5.42 # Proof object total steps : 186
% 1.24/5.42 # Proof object clause steps : 123
% 1.24/5.42 # Proof object formula steps : 63
% 1.24/5.42 # Proof object conjectures : 57
% 1.24/5.42 # Proof object clause conjectures : 54
% 1.24/5.42 # Proof object formula conjectures : 3
% 1.24/5.42 # Proof object initial clauses used : 40
% 1.24/5.42 # Proof object initial formulas used : 31
% 1.24/5.42 # Proof object generating inferences : 65
% 1.24/5.42 # Proof object simplifying inferences : 110
% 1.24/5.42 # Training examples: 0 positive, 0 negative
% 1.24/5.42 # Parsed axioms : 19023
% 1.24/5.42 # Removed by relevancy pruning/SinE : 18922
% 1.24/5.42 # Initial clauses : 145
% 1.24/5.42 # Removed in clause preprocessing : 3
% 1.24/5.42 # Initial clauses in saturation : 142
% 1.24/5.42 # Processed clauses : 8047
% 1.24/5.42 # ...of these trivial : 410
% 1.24/5.42 # ...subsumed : 6279
% 1.24/5.42 # ...remaining for further processing : 1357
% 1.24/5.42 # Other redundant clauses eliminated : 340
% 1.24/5.42 # Clauses deleted for lack of memory : 0
% 1.24/5.42 # Backward-subsumed : 165
% 1.24/5.42 # Backward-rewritten : 292
% 1.24/5.42 # Generated clauses : 144627
% 1.24/5.42 # ...of the previous two non-trivial : 119440
% 1.24/5.42 # Contextual simplify-reflections : 1599
% 1.24/5.42 # Paramodulations : 144246
% 1.24/5.42 # Factorizations : 14
% 1.24/5.42 # Equation resolutions : 365
% 1.24/5.42 # Current number of processed clauses : 896
% 1.24/5.42 # Positive orientable unit clauses : 166
% 1.24/5.42 # Positive unorientable unit clauses: 26
% 1.24/5.42 # Negative unit clauses : 63
% 1.24/5.42 # Non-unit-clauses : 641
% 1.24/5.42 # Current number of unprocessed clauses: 89980
% 1.24/5.42 # ...number of literals in the above : 191456
% 1.24/5.42 # Current number of archived formulas : 0
% 1.24/5.42 # Current number of archived clauses : 460
% 1.24/5.42 # Clause-clause subsumption calls (NU) : 241626
% 1.24/5.42 # Rec. Clause-clause subsumption calls : 197307
% 1.24/5.42 # Non-unit clause-clause subsumptions : 4519
% 1.24/5.42 # Unit Clause-clause subsumption calls : 5459
% 1.24/5.42 # Rewrite failures with RHS unbound : 0
% 1.24/5.42 # BW rewrite match attempts : 2122
% 1.24/5.42 # BW rewrite match successes : 310
% 1.24/5.42 # Condensation attempts : 0
% 1.24/5.42 # Condensation successes : 0
% 1.24/5.42 # Termbank termtop insertions : 2566965
% 1.24/5.42
% 1.24/5.42 # -------------------------------------------------
% 1.24/5.42 # User time : 3.374 s
% 1.24/5.42 # System time : 0.057 s
% 1.24/5.42 # Total time : 3.431 s
% 1.24/5.42 # Maximum resident set size: 101956 pages
% 1.24/24.40 eprover: CPU time limit exceeded, terminating
% 1.24/24.40 eprover: CPU time limit exceeded, terminating
% 1.24/24.41 eprover: CPU time limit exceeded, terminating
% 1.24/24.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.43 eprover: No such file or directory
% 1.24/24.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.43 eprover: No such file or directory
% 1.24/24.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.43 eprover: No such file or directory
% 1.24/24.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.43 eprover: No such file or directory
% 1.24/24.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.43 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.44 eprover: No such file or directory
% 1.24/24.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.45 eprover: No such file or directory
% 1.24/24.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.45 eprover: No such file or directory
% 1.24/24.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.45 eprover: No such file or directory
% 1.24/24.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.45 eprover: No such file or directory
% 1.24/24.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.45 eprover: No such file or directory
% 1.24/24.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.45 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.46 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.47 eprover: No such file or directory
% 1.24/24.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.24/24.48 eprover: No such file or directory
%------------------------------------------------------------------------------