TSTP Solution File: SEU131+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU131+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n031.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 : Thu Aug 31 16:22:37 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 52 ( 10 unt; 12 typ; 0 def)
% Number of atoms : 110 ( 26 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 117 ( 47 ~; 51 |; 11 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 79 ( 8 sgn; 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
subset: ( $i * $i ) > $o ).
tff(decl_24,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
esk3_0: $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
tff(decl_32,type,
esk6_0: $i ).
tff(decl_33,type,
esk7_2: ( $i * $i ) > $i ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
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(l32_xboole_1,conjecture,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( in(X16,X13)
| ~ in(X16,X15)
| X15 != set_difference(X13,X14) )
& ( ~ in(X16,X14)
| ~ in(X16,X15)
| X15 != set_difference(X13,X14) )
& ( ~ in(X17,X13)
| in(X17,X14)
| in(X17,X15)
| X15 != set_difference(X13,X14) )
& ( ~ in(esk2_3(X18,X19,X20),X20)
| ~ in(esk2_3(X18,X19,X20),X18)
| in(esk2_3(X18,X19,X20),X19)
| X20 = set_difference(X18,X19) )
& ( in(esk2_3(X18,X19,X20),X18)
| in(esk2_3(X18,X19,X20),X20)
| X20 = set_difference(X18,X19) )
& ( ~ in(esk2_3(X18,X19,X20),X19)
| in(esk2_3(X18,X19,X20),X20)
| X20 = set_difference(X18,X19) ) ),
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)],[c_0_6])])])])])]) ).
cnf(c_0_8,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_9,plain,
! [X31] : set_difference(empty_set,X31) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_10,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ subset(X7,X8)
| ~ in(X9,X7)
| in(X9,X8) )
& ( in(esk1_2(X10,X11),X10)
| subset(X10,X11) )
& ( ~ in(esk1_2(X10,X11),X11)
| subset(X10,X11) ) ),
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_13,plain,
( ~ in(X1,empty_set)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[l32_xboole_1]) ).
cnf(c_0_16,plain,
( subset(empty_set,X1)
| ~ in(esk1_2(empty_set,X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,negated_conjecture,
( ( set_difference(esk3_0,esk4_0) != empty_set
| ~ subset(esk3_0,esk4_0) )
& ( set_difference(esk3_0,esk4_0) = empty_set
| subset(esk3_0,esk4_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_18,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( set_difference(esk3_0,esk4_0) = empty_set
| subset(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
~ in(X1,empty_set),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_13]) ).
cnf(c_0_22,plain,
( in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_23,plain,
! [X33,X34] :
( ~ in(X33,X34)
| ~ empty(X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_24,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( set_difference(esk3_0,esk4_0) = empty_set
| in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_26,plain,
( set_difference(X1,X2) = empty_set
| in(esk2_3(X1,X2,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( in(esk2_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
( set_difference(esk3_0,esk4_0) = empty_set
| set_difference(esk3_0,X1) = empty_set
| in(esk2_3(esk3_0,X1,empty_set),esk4_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| ~ empty(set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
set_difference(esk3_0,esk4_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21]) ).
cnf(c_0_33,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
( set_difference(esk3_0,esk4_0) != empty_set
| ~ subset(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,negated_conjecture,
( subset(X1,esk4_0)
| ~ in(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ subset(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_14]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU131+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:35:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.015000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.018000 s
%------------------------------------------------------------------------------