TSTP Solution File: SET825-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 14:35:44 EDT 2023
% Result : Unsatisfiable 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 18
% Syntax : Number of formulae : 28 ( 8 unt; 12 typ; 0 def)
% Number of atoms : 28 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
c_Relation_OId: $i ).
tff(decl_24,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_25,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
v_n: $i ).
tff(decl_27,type,
v_Q: $i > $o ).
tff(decl_28,type,
v_m: $i ).
tff(decl_29,type,
tc_nat: $i ).
tff(decl_30,type,
v_x: $i > $i ).
tff(decl_31,type,
v_xa: $i > $i ).
tff(decl_32,type,
c_0: $i ).
tff(decl_33,type,
c_Suc: $i > $i ).
cnf(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Relation_OIdI_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_1,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
cls_Relation_Opair__in__Id__conv__iff1_0 ).
cnf(c_0_7,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
cls_conjecture_2 ).
cnf(c_0_8,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
cls_Relation_OIdI_0 ).
cnf(c_0_9,negated_conjecture,
( v_xa(c_Relation_OId) = v_x(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_10,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
cls_conjecture_3 ).
cnf(c_0_11,negated_conjecture,
( v_xa(c_Relation_OId) = v_x(c_Relation_OId)
| v_m = v_n ),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
~ v_Q(v_m),
cls_conjecture_1 ).
cnf(c_0_13,negated_conjecture,
v_m = v_n,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]),c_0_8])]),c_0_6]) ).
cnf(c_0_14,negated_conjecture,
v_Q(v_n),
cls_conjecture_0 ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:17:09 EDT 2023
% 0.13/0.35 % 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 : 0.003000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.006000 s
%------------------------------------------------------------------------------