TSTP Solution File: SET012-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET012-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 14:32:01 EDT 2023
% Result : Unsatisfiable 0.65s 0.66s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 58 ( 16 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
little_set: $i > $o ).
tff(decl_24,type,
f1: ( $i * $i ) > $i ).
tff(decl_25,type,
complement: $i > $i ).
tff(decl_26,type,
empty_set: $i ).
tff(decl_27,type,
universal_set: $i ).
tff(decl_28,type,
as: $i ).
tff(decl_29,type,
bs: $i ).
tff(decl_30,type,
cs: $i ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
cnf(complement_of_a_is_b,hypothesis,
complement(as) = bs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_is_b) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
cnf(complement_of_b_is_c,hypothesis,
complement(bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_b_is_c) ).
cnf(extensionality1,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(prove_a_equals_c,negated_conjecture,
as != cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_c) ).
cnf(c_0_9,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_10,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_11,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_12,hypothesis,
complement(as) = bs,
complement_of_a_is_b ).
cnf(c_0_13,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_14,hypothesis,
complement(bs) = cs,
complement_of_b_is_c ).
cnf(c_0_15,plain,
( X1 = complement(X2)
| member(f1(X1,complement(X2)),X2)
| ~ member(f1(X1,complement(X2)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_16,hypothesis,
( member(X1,as)
| member(X1,bs)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_17,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
extensionality1 ).
cnf(c_0_18,hypothesis,
( ~ member(X1,cs)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_20,hypothesis,
( X1 = cs
| member(f1(X1,cs),bs)
| ~ member(f1(X1,cs),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_21,hypothesis,
( X1 = X2
| member(f1(X1,X2),bs)
| member(f1(X1,X2),as) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
as != cs,
prove_a_equals_c ).
cnf(c_0_23,hypothesis,
( X1 = cs
| member(f1(X1,cs),X1)
| ~ member(f1(X1,cs),bs) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,hypothesis,
member(f1(as,cs),bs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,hypothesis,
( ~ member(X1,bs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_26,hypothesis,
member(f1(as,cs),as),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22]) ).
cnf(c_0_27,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET012-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n009.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 : Sat Aug 26 13:35:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.57/0.63 start to proof: theBenchmark
% 0.65/0.66 % Version : CSE_E---1.5
% 0.65/0.66 % Problem : theBenchmark.p
% 0.65/0.66 % Proof found
% 0.65/0.66 % SZS status Theorem for theBenchmark.p
% 0.65/0.66 % SZS output start Proof
% See solution above
% 0.65/0.66 % Total time : 0.008000 s
% 0.65/0.66 % SZS output end Proof
% 0.65/0.66 % Total time : 0.011000 s
%------------------------------------------------------------------------------