TSTP Solution File: SET016-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 14:32:07 EDT 2023
% Result : Unsatisfiable 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 34 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
singleton_set: $i > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
m1: $i ).
tff(decl_27,type,
r1: $i ).
tff(decl_28,type,
m2: $i ).
tff(decl_29,type,
r2: $i ).
cnf(equal_ordered_pairs,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = unordered_pair(singleton_set(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
cnf(unordered_pair_1,axiom,
member(X1,unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).
cnf(unordered_pair_3,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).
cnf(singleton_2,axiom,
( X1 = X2
| ~ member(X1,singleton_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).
cnf(singleton_1,axiom,
member(X1,singleton_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).
cnf(prove_first_components_equal,negated_conjecture,
m1 != m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_components_equal) ).
cnf(c_0_7,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
equal_ordered_pairs ).
cnf(c_0_8,axiom,
ordered_pair(X1,X2) = unordered_pair(singleton_set(X1),unordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_9,axiom,
member(X1,unordered_pair(X1,X2)),
unordered_pair_1 ).
cnf(c_0_10,hypothesis,
unordered_pair(singleton_set(m2),unordered_pair(m2,r2)) = unordered_pair(singleton_set(m1),unordered_pair(m1,r1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_3 ).
cnf(c_0_12,hypothesis,
member(singleton_set(m1),unordered_pair(singleton_set(m2),unordered_pair(m2,r2))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
( X1 = X2
| ~ member(X1,singleton_set(X2)) ),
singleton_2 ).
cnf(c_0_14,hypothesis,
( singleton_set(m1) = unordered_pair(m2,r2)
| singleton_set(m1) = singleton_set(m2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,hypothesis,
( singleton_set(m1) = unordered_pair(m2,r2)
| X1 = m1
| ~ member(X1,singleton_set(m2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
member(X1,singleton_set(X1)),
singleton_1 ).
cnf(c_0_17,negated_conjecture,
m1 != m2,
prove_first_components_equal ).
cnf(c_0_18,hypothesis,
singleton_set(m1) = unordered_pair(m2,r2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_19,hypothesis,
member(m1,unordered_pair(m2,r2)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_20,hypothesis,
r2 = m1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_17]) ).
cnf(c_0_21,hypothesis,
singleton_set(m1) = unordered_pair(m2,m1),
inference(rw,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_22,hypothesis,
( X1 = m1
| ~ member(X1,unordered_pair(m2,m1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_23,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_9]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.35 % Computer : n018.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 13:15:15 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.004000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.007000 s
%------------------------------------------------------------------------------