%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG226+2 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 : 300s
% DateTime : Tue May 5 04:08:19 PM UTC 2026
% Result : Theorem 272.06s 177.40s
% Output : CNFRefutation 272.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 81 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 76 ( 26 ~; 19 |; 17 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_closure3,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( v2_relat_1(X2)
& m1_pboole(X2,X1) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure3) ).
fof(t7_closure3,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( v2_relat_1(X2)
& m1_pboole(X2,X1) )
=> ! [X3] :
( ( v2_relat_1(X3)
& m1_pboole(X3,X1) )
=> ( ( k1_closure3(X1,X2) = k1_closure3(X1,X3)
& k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3)) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_closure3) ).
fof(d6_pboole,axiom,
! [X1] : k1_pboole(X1) = k2_funcop_1(X1,k1_xboole_0),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+80.ax',d6_pboole) ).
fof(d2_funcop_1,axiom,
! [X1,X2] : k2_funcop_1(X1,X2) = k2_zfmisc_1(X1,k1_tarski(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+24.ax',d2_funcop_1) ).
fof(redefinition_r6_pboole,axiom,
! [X1,X2,X3] :
( ( m1_pboole(X2,X1)
& m1_pboole(X3,X1) )
=> ( r6_pboole(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+80.ax',redefinition_r6_pboole) ).
fof(c_0_5,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( v2_relat_1(X2)
& m1_pboole(X2,X1) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
inference(fof_simplification,[status(thm)],[t6_closure3]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( v2_relat_1(X2)
& m1_pboole(X2,X1) )
=> ! [X3] :
( ( v2_relat_1(X3)
& m1_pboole(X3,X1) )
=> ( ( k1_closure3(X1,X2) = k1_closure3(X1,X3)
& k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3)) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t7_closure3])]) ).
fof(c_0_7,plain,
! [X1562,X1563] :
( v1_xboole_0(X1562)
| ~ v2_relat_1(X1563)
| ~ m1_pboole(X1563,X1562)
| X1563 = k1_funct_4(k1_pboole(X1562),k7_relat_1(X1563,k1_closure3(X1562,X1563))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X2680] : k1_pboole(X2680) = k2_funcop_1(X2680,k1_xboole_0),
inference(variable_rename,[status(thm)],[d6_pboole]) ).
fof(c_0_9,plain,
! [X2741,X2742] : k2_funcop_1(X2741,X2742) = k2_zfmisc_1(X2741,k1_tarski(X2742)),
inference(variable_rename,[status(thm)],[d2_funcop_1]) ).
fof(c_0_10,negated_conjecture,
( ~ v1_xboole_0(esk1_0)
& v2_relat_1(esk2_0)
& m1_pboole(esk2_0,esk1_0)
& v2_relat_1(esk3_0)
& m1_pboole(esk3_0,esk1_0)
& k1_closure3(esk1_0,esk2_0) = k1_closure3(esk1_0,esk3_0)
& k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk3_0,k1_closure3(esk1_0,esk3_0))
& ~ r6_pboole(esk1_0,esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( v1_xboole_0(X1)
| X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2)))
| ~ v2_relat_1(X2)
| ~ m1_pboole(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
k1_pboole(X1) = k2_funcop_1(X1,k1_xboole_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
k2_funcop_1(X1,X2) = k2_zfmisc_1(X1,k1_tarski(X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk3_0,k1_closure3(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
k1_closure3(esk1_0,esk2_0) = k1_closure3(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( X2 = k1_funct_4(k2_zfmisc_1(X1,k1_tarski(k1_xboole_0)),k7_relat_1(X2,k1_closure3(X1,X2)))
| v1_xboole_0(X1)
| ~ v2_relat_1(X2)
| ~ m1_pboole(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_17,negated_conjecture,
k7_relat_1(esk3_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
m1_pboole(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
v2_relat_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
k1_funct_4(k2_zfmisc_1(esk1_0,k1_tarski(k1_xboole_0)),k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0))) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_22,negated_conjecture,
m1_pboole(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
v2_relat_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_24,plain,
! [X1448,X1449,X1450] :
( ( ~ r6_pboole(X1448,X1449,X1450)
| X1449 = X1450
| ~ m1_pboole(X1449,X1448)
| ~ m1_pboole(X1450,X1448) )
& ( X1449 != X1450
| r6_pboole(X1448,X1449,X1450)
| ~ m1_pboole(X1449,X1448)
| ~ m1_pboole(X1450,X1448) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r6_pboole])])]) ).
cnf(c_0_25,negated_conjecture,
~ r6_pboole(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
esk3_0 = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_22]),c_0_23])]),c_0_20]) ).
cnf(c_0_27,plain,
( r6_pboole(X3,X1,X2)
| X1 != X2
| ~ m1_pboole(X1,X3)
| ~ m1_pboole(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
~ r6_pboole(esk1_0,esk2_0,esk2_0),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( r6_pboole(X1,X2,X2)
| ~ m1_pboole(X2,X1) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG226+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:25:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 272.06/177.40 % Version : CSE_E---1.7
% 272.06/177.40 % Problem : theBenchmark.p
% 272.06/177.40 % SZS status Theorem for theBenchmark.p
% 272.06/177.40 % SZS output start CNFRefutation
% See solution above
% 272.86/178.29 % Total time : 144.573s
%------------------------------------------------------------------------------