%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU427+3 : 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 : n023.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 05:12:18 PM UTC 2026
% Result : Theorem 55.75s 38.77s
% Output : CNFRefutation 55.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 21 unt; 0 def)
% Number of atoms : 80 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 71 ( 28 ~; 24 |; 6 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_relset_2,conjecture,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X1))
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( k4_relset_2(k1_zfmisc_1(X1),X2,k6_relset_2(X2,X1,X5),k3_pua2mss1(X3)) = k1_xboole_0
=> k8_relset_2(X1,X2,k4_subset_1(X1,X3,X4),X5) = k8_relset_2(X1,X2,X4,X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relset_2) ).
fof(t23_relset_2,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( k4_relset_2(k1_zfmisc_1(X1),X2,k6_relset_2(X2,X1,X4),k3_pua2mss1(X3)) = k1_xboole_0
<=> X3 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_2) ).
fof(d2_pua2mss1,axiom,
! [X1] : k3_pua2mss1(X1) = k8_eqrel_1(X1,k6_partfun1(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+441.ax',d2_pua2mss1) ).
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(t93_zfmisc_1,axiom,
! [X1,X2] : k3_tarski(k2_tarski(X1,X2)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t93_zfmisc_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> k4_subset_1(X1,X2,X3) = k2_xboole_0(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',redefinition_k4_subset_1) ).
fof(t4_subset_1,axiom,
! [X1] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',t4_subset_1) ).
fof(t2_xboole_1,axiom,
! [X1] : r1_tarski(k1_xboole_0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t2_xboole_1) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X1))
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( k4_relset_2(k1_zfmisc_1(X1),X2,k6_relset_2(X2,X1,X5),k3_pua2mss1(X3)) = k1_xboole_0
=> k8_relset_2(X1,X2,k4_subset_1(X1,X3,X4),X5) = k8_relset_2(X1,X2,X4,X5) ) ) ) ),
inference(assume_negation,[status(cth)],[t26_relset_2]) ).
fof(c_0_9,plain,
! [X1492,X1493,X1494,X1495] :
( ( k4_relset_2(k1_zfmisc_1(X1492),X1493,k6_relset_2(X1493,X1492,X1495),k3_pua2mss1(X1494)) != k1_xboole_0
| X1494 = k1_xboole_0
| ~ m1_subset_1(X1495,k1_zfmisc_1(k2_zfmisc_1(X1492,X1493)))
| ~ m1_subset_1(X1494,k1_zfmisc_1(X1492)) )
& ( X1494 != k1_xboole_0
| k4_relset_2(k1_zfmisc_1(X1492),X1493,k6_relset_2(X1493,X1492,X1495),k3_pua2mss1(X1494)) = k1_xboole_0
| ~ m1_subset_1(X1495,k1_zfmisc_1(k2_zfmisc_1(X1492,X1493)))
| ~ m1_subset_1(X1494,k1_zfmisc_1(X1492)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_relset_2])])])]) ).
fof(c_0_10,plain,
! [X1496] : k3_pua2mss1(X1496) = k8_eqrel_1(X1496,k6_partfun1(X1496)),
inference(variable_rename,[status(thm)],[d2_pua2mss1]) ).
fof(c_0_11,negated_conjecture,
( m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0))
& m1_subset_1(esk4_0,k1_zfmisc_1(esk1_0))
& m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))
& k4_relset_2(k1_zfmisc_1(esk1_0),esk2_0,k6_relset_2(esk2_0,esk1_0,esk5_0),k3_pua2mss1(esk3_0)) = k1_xboole_0
& k8_relset_2(esk1_0,esk2_0,k4_subset_1(esk1_0,esk3_0,esk4_0),esk5_0) != k8_relset_2(esk1_0,esk2_0,esk4_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( X4 = k1_xboole_0
| k4_relset_2(k1_zfmisc_1(X1),X2,k6_relset_2(X2,X1,X3),k3_pua2mss1(X4)) != k1_xboole_0
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_subset_1(X4,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
k3_pua2mss1(X1) = k8_eqrel_1(X1,k6_partfun1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
k4_relset_2(k1_zfmisc_1(esk1_0),esk2_0,k6_relset_2(esk2_0,esk1_0,esk5_0),k3_pua2mss1(esk3_0)) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X2123,X2124] :
( ~ r1_tarski(X2123,X2124)
| k2_xboole_0(X2123,X2124) = X2124 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_16,plain,
! [X2513,X2514] : k3_tarski(k2_tarski(X2513,X2514)) = k2_xboole_0(X2513,X2514),
inference(variable_rename,[status(thm)],[t93_zfmisc_1]) ).
fof(c_0_17,plain,
! [X1402,X1403,X1404] :
( ~ m1_subset_1(X1403,k1_zfmisc_1(X1402))
| ~ m1_subset_1(X1404,k1_zfmisc_1(X1402))
| k4_subset_1(X1402,X1403,X1404) = k2_xboole_0(X1403,X1404) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_18,plain,
( X4 = k1_xboole_0
| k4_relset_2(k1_zfmisc_1(X1),X2,k6_relset_2(X2,X1,X3),k8_eqrel_1(X4,k6_partfun1(X4))) != k1_xboole_0
| ~ m1_subset_1(X4,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
k4_relset_2(k1_zfmisc_1(esk1_0),esk2_0,k6_relset_2(esk2_0,esk1_0,esk5_0),k8_eqrel_1(esk3_0,k6_partfun1(esk3_0))) = k1_xboole_0,
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( k2_xboole_0(X1,X2) = X2
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
k3_tarski(k2_tarski(X1,X2)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( k4_subset_1(X2,X1,X3) = k2_xboole_0(X1,X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
k8_relset_2(esk1_0,esk2_0,k4_subset_1(esk1_0,esk3_0,esk4_0),esk5_0) != k8_relset_2(esk1_0,esk2_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
esk3_0 = k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_27,plain,
( k3_tarski(k2_tarski(X1,X2)) = X2
| ~ r1_tarski(X1,X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( k4_subset_1(X2,X1,X3) = k3_tarski(k2_tarski(X1,X3))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
fof(c_0_29,plain,
! [X1450] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1450)),
inference(variable_rename,[status(thm)],[t4_subset_1]) ).
fof(c_0_30,plain,
! [X1430] : r1_tarski(k1_xboole_0,X1430),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_31,negated_conjecture,
k8_relset_2(esk1_0,esk2_0,k4_subset_1(esk1_0,k1_xboole_0,esk4_0),esk5_0) != k8_relset_2(esk1_0,esk2_0,esk4_0,esk5_0),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( k4_subset_1(X1,X2,X3) = X3
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ r1_tarski(X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
r1_tarski(k1_xboole_0,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU427+3 : TPTP v9.2.1. Released v3.4.0.
% 0.13/0.13 % 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
% 0.18/0.34 % Computer : n023.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 03:12:41 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.36 % start to proof: theBenchmark
% 55.75/38.77 % Version : CSE_E---1.7
% 55.75/38.77 % Problem : theBenchmark.p
% 55.75/38.77 % SZS status Theorem for theBenchmark.p
% 55.75/38.77 % SZS output start CNFRefutation
% See solution above
% 55.95/38.92 % Total time : 33.255s
%------------------------------------------------------------------------------