%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU422+3 : 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 : n010.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 05:12:16 PM UTC 2026
% Result : Theorem 23.48s 20.95s
% Output : CNFRefutation 23.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 94 ( 5 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 88 ( 35 ~; 25 |; 9 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 1 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t16_relset_2,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(t79_zfmisc_1,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
=> r1_tarski(k1_zfmisc_1(X1),k1_zfmisc_1(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+6.ax',t79_zfmisc_1) ).
fof(t15_relset_2,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> X2 = k3_tarski(a_2_0_relset_2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_2) ).
fof(t100_zfmisc_1,axiom,
! [X1] : r1_tarski(X1,k1_zfmisc_1(k3_tarski(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+6.ax',t100_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) )
& ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',fc1_subset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t16_relset_2])]) ).
fof(c_0_9,plain,
! [X2559,X2560] :
( ( ~ m1_subset_1(X2559,k1_zfmisc_1(X2560))
| r1_tarski(X2559,X2560) )
& ( ~ r1_tarski(X2559,X2560)
| m1_subset_1(X2559,k1_zfmisc_1(X2560)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_10,negated_conjecture,
( ~ v1_xboole_0(esk1_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0))
& ~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X2536,X2537] :
( ~ r1_tarski(X2536,X2537)
| r1_tarski(k1_zfmisc_1(X2536),k1_zfmisc_1(X2537)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t79_zfmisc_1])]) ).
cnf(c_0_12,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> X2 = k3_tarski(a_2_0_relset_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[t15_relset_2]) ).
cnf(c_0_15,plain,
( r1_tarski(k1_zfmisc_1(X1),k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
r1_tarski(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X2461] : r1_tarski(X2461,k1_zfmisc_1(k3_tarski(X2461))),
inference(variable_rename,[status(thm)],[t100_zfmisc_1]) ).
fof(c_0_18,plain,
! [X2212,X2213] :
( v1_xboole_0(X2212)
| ~ m1_subset_1(X2213,k1_zfmisc_1(X2212))
| X2213 = k3_tarski(a_2_0_relset_2(X2212,X2213)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_19,negated_conjecture,
r1_tarski(k1_zfmisc_1(esk2_0),k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) )
& ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
cnf(c_0_21,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
r1_tarski(X1,k1_zfmisc_1(k3_tarski(X1))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( v1_xboole_0(X1)
| X2 = k3_tarski(a_2_0_relset_2(X1,X2))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_25,plain,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_26,plain,
! [X2201,X2202,X2203] :
( ~ r2_hidden(X2201,X2202)
| ~ m1_subset_1(X2202,k1_zfmisc_1(X2203))
| m1_subset_1(X2201,X2203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_27,negated_conjecture,
r1_tarski(k1_zfmisc_1(k1_zfmisc_1(esk2_0)),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
fof(c_0_28,plain,
! [X2220,X2221] :
( ( ~ m1_subset_1(X2221,X2220)
| r2_hidden(X2221,X2220)
| v1_xboole_0(X2220) )
& ( ~ r2_hidden(X2221,X2220)
| m1_subset_1(X2221,X2220)
| v1_xboole_0(X2220) )
& ( ~ m1_subset_1(X2221,X2220)
| v1_xboole_0(X2221)
| ~ v1_xboole_0(X2220) )
& ( ~ v1_xboole_0(X2221)
| m1_subset_1(X2221,X2220)
| ~ v1_xboole_0(X2220) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_29,plain,
m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(k3_tarski(X1)))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
k3_tarski(a_2_0_relset_2(esk1_0,esk2_0)) = esk2_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_13]),c_0_24]) ).
fof(c_0_31,plain,
! [X2185] : ~ v1_xboole_0(k1_zfmisc_1(X2185)),
inference(variable_rename,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
m1_subset_1(k1_zfmisc_1(k1_zfmisc_1(esk2_0)),k1_zfmisc_1(k1_zfmisc_1(k1_zfmisc_1(esk1_0)))),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_34,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk2_0))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
| ~ r2_hidden(X1,k1_zfmisc_1(k1_zfmisc_1(esk2_0))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
r2_hidden(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk2_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU422+3 : 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
% 0.17/0.33 % Computer : n010.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 03:08:39 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 23.48/20.95 % Version : CSE_E---1.7
% 23.48/20.95 % Problem : theBenchmark.p
% 23.48/20.95 % SZS status Theorem for theBenchmark.p
% 23.48/20.95 % SZS output start CNFRefutation
% See solution above
% 23.48/20.96 % Total time : 19.851s
%------------------------------------------------------------------------------