%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU418+2 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 05:12:14 PM UTC 2026
% Result : Theorem 3.73s 3.49s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 22 unt; 0 def)
% Number of atoms : 84 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 75 ( 32 ~; 25 |; 4 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 2 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_relset_2,conjecture,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_2) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t48_xboole_1) ).
fof(t19_xboole_1,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X1,X2)
& r1_tarski(X1,X3) )
=> r1_tarski(X1,k3_xboole_0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t19_xboole_1) ).
fof(t49_relat_1,axiom,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> ( r1_tarski(X1,X2)
=> r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t49_relat_1) ).
fof(t3_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> v1_relat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t3_relat_1) ).
fof(t36_xboole_1,axiom,
! [X1,X2] : r1_tarski(k4_xboole_0(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t36_xboole_1) ).
fof(t43_xboole_1,axiom,
! [X1,X2,X3] :
( r1_tarski(X1,k2_xboole_0(X2,X3))
=> r1_tarski(k4_xboole_0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t43_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t39_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : r1_tarski(X1,k2_xboole_0(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t7_xboole_1) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
inference(assume_negation,[status(cth)],[t8_relset_2]) ).
fof(c_0_11,negated_conjecture,
( v1_relat_1(esk1_0)
& v1_relat_1(esk2_0)
& v1_relat_1(esk3_0)
& ~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k3_xboole_0(k5_relat_1(esk1_0,esk3_0),k5_relat_1(esk2_0,esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
! [X1122,X1123] : k4_xboole_0(X1122,k4_xboole_0(X1122,X1123)) = k3_xboole_0(X1122,X1123),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_13,plain,
! [X1082,X1083,X1084] :
( ~ r1_tarski(X1082,X1083)
| ~ r1_tarski(X1082,X1084)
| r1_tarski(X1082,k3_xboole_0(X1083,X1084)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
cnf(c_0_14,negated_conjecture,
~ r1_tarski(k5_relat_1(k3_xboole_0(esk1_0,esk2_0),esk3_0),k3_xboole_0(k5_relat_1(esk1_0,esk3_0),k5_relat_1(esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( r1_tarski(X1,k3_xboole_0(X2,X3))
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X1231,X1232,X1233] :
( ~ v1_relat_1(X1231)
| ~ v1_relat_1(X1232)
| ~ v1_relat_1(X1233)
| ~ r1_tarski(X1231,X1232)
| r1_tarski(k5_relat_1(X1231,X1233),k5_relat_1(X1232,X1233)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t49_relat_1])])]) ).
fof(c_0_18,plain,
! [X1023,X1024] :
( ~ v1_relat_1(X1024)
| ~ r1_tarski(X1023,X1024)
| v1_relat_1(X1023) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_relat_1])]) ).
cnf(c_0_19,negated_conjecture,
~ r1_tarski(k5_relat_1(k4_xboole_0(esk1_0,k4_xboole_0(esk1_0,esk2_0)),esk3_0),k4_xboole_0(k5_relat_1(esk1_0,esk3_0),k4_xboole_0(k5_relat_1(esk1_0,esk3_0),k5_relat_1(esk2_0,esk3_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_20,plain,
( r1_tarski(X1,k4_xboole_0(X2,k4_xboole_0(X2,X3)))
| ~ r1_tarski(X1,X3)
| ~ r1_tarski(X1,X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_21,plain,
( r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X3)
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ r1_tarski(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk1_0,k4_xboole_0(esk1_0,esk2_0)),esk3_0),k5_relat_1(esk2_0,esk3_0))
| ~ r1_tarski(k5_relat_1(k4_xboole_0(esk1_0,k4_xboole_0(esk1_0,esk2_0)),esk3_0),k5_relat_1(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( r1_tarski(k5_relat_1(X1,X2),k5_relat_1(X3,X2))
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X3)
| ~ r1_tarski(X1,X3) ),
inference(csr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
v1_relat_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
v1_relat_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_27,plain,
! [X1504,X1505] : r1_tarski(k4_xboole_0(X1504,X1505),X1504),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_28,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk1_0,k4_xboole_0(esk1_0,esk2_0)),esk3_0),k5_relat_1(esk1_0,esk3_0))
| ~ r1_tarski(k4_xboole_0(esk1_0,k4_xboole_0(esk1_0,esk2_0)),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
v1_relat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
r1_tarski(k4_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_31,plain,
! [X1420,X1421,X1422] :
( ~ r1_tarski(X1420,k2_xboole_0(X1421,X1422))
| r1_tarski(k4_xboole_0(X1420,X1421),X1422) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_xboole_1])]) ).
fof(c_0_32,plain,
! [X1372,X1373] : k2_xboole_0(X1372,X1373) = k2_xboole_0(X1373,X1372),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_33,plain,
! [X1410,X1411] : k2_xboole_0(X1410,k4_xboole_0(X1411,X1410)) = k2_xboole_0(X1410,X1411),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_34,plain,
! [X1384,X1385] : r1_tarski(X1384,k2_xboole_0(X1384,X1385)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_35,negated_conjecture,
~ r1_tarski(k4_xboole_0(esk1_0,k4_xboole_0(esk1_0,esk2_0)),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_25]),c_0_29]),c_0_30])]) ).
cnf(c_0_36,plain,
( r1_tarski(k4_xboole_0(X1,X2),X3)
| ~ r1_tarski(X1,k2_xboole_0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
r1_tarski(X1,k2_xboole_0(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]),c_0_37]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU418+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n007.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 03:07:09 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.73/3.49 % Version : CSE_E---1.7
% 3.73/3.49 % Problem : theBenchmark.p
% 3.73/3.49 % SZS status Theorem for theBenchmark.p
% 3.73/3.49 % SZS output start CNFRefutation
% See solution above
% 3.73/3.49 % Total time : 2.864s
%------------------------------------------------------------------------------