%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU110+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n002.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 05:10:38 PM UTC 2026
% Result : Theorem 1.40s 1.75s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 107 ( 10 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 120 ( 48 ~; 54 |; 10 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 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 : 66 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_finsub_1,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> subset(finite_subsets(X1),finite_subsets(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> subset(finite_subsets(X1),finite_subsets(X2)) ),
inference(assume_negation,[status(cth)],[t23_finsub_1]) ).
fof(c_0_7,plain,
! [X106,X107,X108] :
( ~ subset(X106,X107)
| ~ subset(X107,X108)
| subset(X106,X108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_8,negated_conjecture,
( subset(esk13_0,esk14_0)
& ~ subset(finite_subsets(esk13_0),finite_subsets(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X78,X79,X80,X81] :
( ( subset(X80,X78)
| ~ in(X80,X79)
| X79 != finite_subsets(X78)
| ~ preboolean(X79) )
& ( finite(X80)
| ~ in(X80,X79)
| X79 != finite_subsets(X78)
| ~ preboolean(X79) )
& ( ~ subset(X81,X78)
| ~ finite(X81)
| in(X81,X79)
| X79 != finite_subsets(X78)
| ~ preboolean(X79) )
& ( ~ in(esk2_2(X78,X79),X79)
| ~ subset(esk2_2(X78,X79),X78)
| ~ finite(esk2_2(X78,X79))
| X79 = finite_subsets(X78)
| ~ preboolean(X79) )
& ( subset(esk2_2(X78,X79),X78)
| in(esk2_2(X78,X79),X79)
| X79 = finite_subsets(X78)
| ~ preboolean(X79) )
& ( finite(esk2_2(X78,X79))
| in(esk2_2(X78,X79),X79)
| X79 = finite_subsets(X78)
| ~ preboolean(X79) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_finsub_1])])])])])]) ).
fof(c_0_10,plain,
! [X83] : preboolean(finite_subsets(X83)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
cnf(c_0_11,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
subset(esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ in(X1,X3)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X72,X73,X74,X75,X76] :
( ( ~ subset(X72,X73)
| ~ in(X74,X72)
| in(X74,X73) )
& ( in(esk1_2(X75,X76),X75)
| subset(X75,X76) )
& ( ~ in(esk1_2(X75,X76),X76)
| subset(X75,X76) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( subset(X1,esk14_0)
| ~ subset(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14])]) ).
cnf(c_0_18,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| ~ finite(X1)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
( subset(X1,esk14_0)
| ~ subset(X2,esk13_0)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_21,plain,
( subset(esk1_2(finite_subsets(X1),X2),X1)
| subset(finite_subsets(X1),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X103] : subset(X103,X103),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( in(X1,finite_subsets(X2))
| ~ subset(X1,X2)
| ~ finite(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_14])]) ).
cnf(c_0_25,negated_conjecture,
( subset(finite_subsets(esk13_0),X1)
| subset(X2,esk14_0)
| ~ subset(X2,esk1_2(finite_subsets(esk13_0),X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( finite(X1)
| ~ in(X1,X2)
| X2 != finite_subsets(X3)
| ~ preboolean(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,plain,
( subset(X1,finite_subsets(X2))
| ~ subset(esk1_2(X1,finite_subsets(X2)),X2)
| ~ finite(esk1_2(X1,finite_subsets(X2))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( subset(esk1_2(finite_subsets(esk13_0),X1),esk14_0)
| subset(finite_subsets(esk13_0),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ subset(finite_subsets(esk13_0),finite_subsets(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,plain,
( finite(X1)
| ~ in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_14])]) ).
cnf(c_0_32,negated_conjecture,
~ finite(esk1_2(finite_subsets(esk13_0),finite_subsets(esk14_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
( subset(finite_subsets(X1),X2)
| finite(esk1_2(finite_subsets(X1),X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU110+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n002.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 03:08:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.40/1.75 % Version : CSE_E---1.7
% 1.40/1.75 % Problem : theBenchmark.p
% 1.40/1.75 % SZS status Theorem for theBenchmark.p
% 1.40/1.75 % SZS output start CNFRefutation
% See solution above
% 1.40/1.76 % Total time : 1.372s
%------------------------------------------------------------------------------