TSTP Solution File: SET601+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 14:34:44 EDT 2023
% Result : Theorem 0.21s 0.76s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 45 ( 36 unt; 9 typ; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% 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 : 76 ( 4 sgn; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
intersection: ( $i * $i ) > $i ).
tff(decl_24,type,
member: ( $i * $i ) > $o ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk3_0: $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
fof(union_distributes_over_intersection,axiom,
! [X1,X2,X3] : union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
fof(union_intersection,axiom,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
fof(associativity_of_intersection,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(prove_th72,conjecture,
! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th72) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(associativity_of_union,axiom,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
fof(idempotency_of_intersection,axiom,
! [X1] : intersection(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_intersection) ).
fof(c_0_8,plain,
! [X13,X14,X15] : union(X13,intersection(X14,X15)) = intersection(union(X13,X14),union(X13,X15)),
inference(variable_rename,[status(thm)],[union_distributes_over_intersection]) ).
fof(c_0_9,plain,
! [X11,X12] : union(X11,intersection(X11,X12)) = X11,
inference(variable_rename,[status(thm)],[union_intersection]) ).
fof(c_0_10,plain,
! [X8,X9,X10] : intersection(intersection(X8,X9),X10) = intersection(X8,intersection(X9,X10)),
inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).
cnf(c_0_11,plain,
union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
union(X1,intersection(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X24,X25] : union(X24,X25) = union(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
inference(assume_negation,[status(cth)],[prove_th72]) ).
cnf(c_0_16,plain,
intersection(X1,union(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_12]) ).
cnf(c_0_17,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,negated_conjecture,
union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_19,plain,
! [X26,X27] : intersection(X26,X27) = intersection(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_20,plain,
! [X4,X5,X6] : union(union(X4,X5),X6) = union(X4,union(X5,X6)),
inference(variable_rename,[status(thm)],[associativity_of_union]) ).
cnf(c_0_21,plain,
intersection(X1,union(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
intersection(union(X1,X2),union(X3,X1)) = union(X1,intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_26,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
intersection(union(esk3_0,esk4_0),intersection(union(esk3_0,esk5_0),union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17]),c_0_13]),c_0_23]),c_0_23]),c_0_24]),c_0_17]) ).
cnf(c_0_28,plain,
intersection(union(X1,X2),union(X3,X2)) = union(X2,intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_29,plain,
intersection(X1,union(X2,intersection(X1,X3))) = intersection(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
fof(c_0_30,plain,
! [X7] : intersection(X7,X7) = X7,
inference(variable_rename,[status(thm)],[idempotency_of_intersection]) ).
cnf(c_0_31,negated_conjecture,
intersection(union(esk3_0,esk4_0),union(esk5_0,intersection(esk3_0,esk4_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
intersection(X1,union(X2,X3)) = union(intersection(X1,X3),intersection(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_12]),c_0_29]) ).
cnf(c_0_33,plain,
intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_34,plain,
intersection(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_23]),c_0_32]),c_0_34]),c_0_17]),c_0_12]),c_0_23]),c_0_23]),c_0_32]),c_0_23]),c_0_23]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:06:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.76 % Version : CSE_E---1.5
% 0.21/0.76 % Problem : theBenchmark.p
% 0.21/0.76 % Proof found
% 0.21/0.76 % SZS status Theorem for theBenchmark.p
% 0.21/0.76 % SZS output start Proof
% See solution above
% 0.21/0.76 % Total time : 0.171000 s
% 0.21/0.76 % SZS output end Proof
% 0.21/0.76 % Total time : 0.174000 s
%------------------------------------------------------------------------------