TSTP Solution File: PUZ062-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : PUZ062-2 : 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 : n012.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 13:12:27 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 61 ( 24 unt; 21 typ; 0 def)
% Number of atoms : 64 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 10 >; 12 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 42 ( 10 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Finite__Set_OFinites: $i ).
tff(decl_23,type,
tc_set: $i > $i ).
tff(decl_24,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_27,type,
c_Suc: $i > $i ).
tff(decl_28,type,
c_inter: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Mutil_Odomino: $i ).
tff(decl_30,type,
tc_nat: $i ).
tff(decl_31,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_32,type,
c_Mutil_Otiling: ( $i * $i ) > $i ).
tff(decl_33,type,
c_emptyset: $i ).
tff(decl_34,type,
v_t: $i ).
tff(decl_35,type,
c_0: $i ).
tff(decl_36,type,
c_Mutil_Ocoloured: $i > $i ).
tff(decl_37,type,
v_a: $i ).
tff(decl_38,type,
v_i: $i ).
tff(decl_39,type,
v_j: $i ).
tff(decl_40,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
v_m: $i ).
tff(decl_42,type,
v_n: $i ).
cnf(cls_Set_OInt__iff_1,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
cnf(cls_conjecture_4,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_5,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Finite__Set_Ocard__insert__disjoint_0,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_insert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Set_OInt__iff_2,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
cnf(cls_conjecture_2,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
cnf(cls_Set_Oinsert__iff_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
cnf(cls_conjecture_3,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Mutil_Otiling__domino__finite_0,axiom,
( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Finite__Set_Ofinite__Int_1,axiom,
( c_in(c_inter(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
cnf(c_0_13,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OInt__iff_1 ).
cnf(c_0_14,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
cls_conjecture_4 ).
cnf(c_0_15,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
cls_conjecture_5 ).
cnf(c_0_16,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_insert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
cls_Finite__Set_Ocard__insert__disjoint_0 ).
cnf(c_0_17,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
cls_conjecture_1 ).
cnf(c_0_18,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
cls_Set_OInt__iff_2 ).
cnf(c_0_19,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
cls_conjecture_2 ).
cnf(c_0_20,axiom,
~ c_in(X1,c_emptyset,X2),
cls_Set_Oempty__iff_0 ).
cnf(c_0_21,negated_conjecture,
( c_in(X1,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X1,c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_Oinsert__iff_1 ).
cnf(c_0_23,negated_conjecture,
( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( ~ c_in(X1,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X1,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
cls_conjecture_3 ).
cnf(c_0_27,negated_conjecture,
( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
cls_Mutil_Otiling__domino__finite_0 ).
cnf(c_0_30,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
cls_conjecture_0 ).
cnf(c_0_31,negated_conjecture,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_27]),c_0_28]) ).
cnf(c_0_33,axiom,
( c_in(c_inter(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
cls_Finite__Set_Ofinite__Int_1 ).
cnf(c_0_34,negated_conjecture,
c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_13,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,negated_conjecture,
~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_36]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ062-2 : 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
% 0.13/0.34 % Computer : n012.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 22:13:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.007000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.010000 s
%------------------------------------------------------------------------------