TSTP Solution File: SET840-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET840-2 : 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 : n001.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 14:35:51 EDT 2023
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 43 ( 8 unt; 9 typ; 0 def)
% Number of atoms : 68 ( 10 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 62 ( 28 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 6 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 10 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_S: $i ).
tff(decl_23,type,
c_emptyset: $i ).
tff(decl_24,type,
t_b: $i ).
tff(decl_25,type,
tc_set: $i > $i ).
tff(decl_26,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
c_Union: ( $i * $i ) > $i ).
tff(decl_29,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
cnf(cls_Set_OinsertE_0,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OUnionI_0,axiom,
( c_in(X1,c_Union(X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OinsertCI_0,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b))
| ~ c_in(X1,v_S,tc_set(t_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_9,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
cls_Set_OinsertE_0 ).
cnf(c_0_10,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_11,axiom,
( c_in(X1,c_Union(X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X2,X4,tc_set(X3)) ),
cls_Set_OUnionI_0 ).
cnf(c_0_12,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_13,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1 ).
cnf(c_0_14,plain,
( c_Main_OsubsetI__1(c_insert(X1,X2,X3),X4,X3) = X1
| c_in(c_Main_OsubsetI__1(c_insert(X1,X2,X3),X4,X3),X2,X3)
| c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OinsertCI_0 ).
cnf(c_0_16,plain,
( c_in(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),X4)
| ~ c_in(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( c_Main_OsubsetI__1(c_insert(X1,X2,X3),X2,X3) = X1
| c_lessequals(c_insert(X1,X2,X3),X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( c_lessequals(X1,c_insert(X2,X3,X4),tc_set(X4))
| ~ c_in(c_Main_OsubsetI__1(X1,c_insert(X2,X3,X4),X4),X3,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_19,plain,
( c_lessequals(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),tc_set(X4))
| ~ c_in(c_Main_OsubsetI__1(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),X4),X2,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_20,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0 ).
cnf(c_0_21,plain,
( c_lessequals(c_insert(X1,X2,X3),X2,tc_set(X3))
| ~ c_in(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_22,plain,
c_lessequals(X1,c_insert(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b))
| ~ c_in(X1,v_S,tc_set(t_b)) ),
cls_conjecture_1 ).
cnf(c_0_24,plain,
c_lessequals(X1,c_Union(c_insert(X1,X2,tc_set(X3)),X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_25,plain,
( c_insert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( X1 = c_Union(v_S,t_b)
| ~ c_in(X1,v_S,tc_set(t_b))
| ~ c_lessequals(X1,c_Union(v_S,t_b),tc_set(t_b)) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_27,plain,
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( X1 = c_Union(v_S,t_b)
| ~ c_in(X1,v_S,tc_set(t_b)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( c_Main_OsubsetI__1(v_S,X1,tc_set(t_b)) = c_Union(v_S,t_b)
| c_lessequals(v_S,X1,tc_set(tc_set(t_b))) ),
inference(spm,[status(thm)],[c_0_28,c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( c_lessequals(v_S,X1,tc_set(tc_set(t_b)))
| ~ c_in(c_Union(v_S,t_b),X1,tc_set(t_b)) ),
inference(spm,[status(thm)],[c_0_13,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
cls_conjecture_0 ).
cnf(c_0_32,negated_conjecture,
c_lessequals(v_S,c_insert(c_Union(v_S,t_b),X1,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(spm,[status(thm)],[c_0_30,c_0_12]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET840-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 11:18:15 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.47 start to proof: theBenchmark
% 0.18/0.48 % Version : CSE_E---1.5
% 0.18/0.48 % Problem : theBenchmark.p
% 0.18/0.48 % Proof found
% 0.18/0.48 % SZS status Theorem for theBenchmark.p
% 0.18/0.48 % SZS output start Proof
% See solution above
% 0.18/0.48 % Total time : 0.005000 s
% 0.18/0.48 % SZS output end Proof
% 0.18/0.48 % Total time : 0.007000 s
%------------------------------------------------------------------------------