TSTP Solution File: SET837-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET837-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 14:35:50 EDT 2023
% Result : Unsatisfiable 0.93s 0.98s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 74 ( 15 unt; 10 typ; 0 def)
% Number of atoms : 144 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 137 ( 57 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 5 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 96 ( 9 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_X: $i ).
tff(decl_23,type,
v_Y: $i ).
tff(decl_24,type,
v_Z: $i ).
tff(decl_25,type,
t_a: $i ).
tff(decl_26,type,
c_union: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
tc_set: $i > $i ).
tff(decl_28,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
v_x: $i ).
tff(decl_30,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
cnf(cls_Set_OUnE_0,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OUnCI_0,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_Z,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Set_OUnCI_1,axiom,
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_5,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_X,X1,tc_set(t_a))
| ~ c_lessequals(v_Z,X1,tc_set(t_a))
| ~ c_lessequals(v_Y,X1,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_0,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_Y,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_4,negated_conjecture,
( ~ c_lessequals(v_X,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(c_0_13,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
cls_Set_OUnE_0 ).
cnf(c_0_14,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_15,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUnCI_0 ).
cnf(c_0_16,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_17,plain,
( c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X4,X3),X1,X3)
| c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X4,X3),X2,X3)
| c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),c_union(X4,X1,X3),X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0 ).
cnf(c_0_20,plain,
( c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X1,X3),X2,X3)
| c_lessequals(c_union(X1,X2,X3),X1,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
c_lessequals(X1,c_union(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_Z,v_X,tc_set(t_a)) ),
cls_conjecture_1 ).
cnf(c_0_23,plain,
( c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X1,X3),X4,X3)
| c_lessequals(c_union(X1,X2,X3),X1,tc_set(X3))
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUnCI_1 ).
cnf(c_0_26,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),X1,t_a),v_X,t_a)
| c_lessequals(c_union(X1,v_Z,t_a),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),c_union(X1,X4,X3),X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_28,plain,
( c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X4,X3),c_union(X5,X2,X3),X3)
| c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X4,X3),X1,X3)
| c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_29,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_30,negated_conjecture,
c_lessequals(c_union(v_X,v_Z,t_a),v_X,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,plain,
c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_X,X1,tc_set(t_a))
| ~ c_lessequals(v_Z,X1,tc_set(t_a))
| ~ c_lessequals(v_Y,X1,tc_set(t_a)) ),
cls_conjecture_5 ).
cnf(c_0_33,plain,
( c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),c_union(X4,X2,X3),X3),X1,X3)
| c_lessequals(c_union(X1,X2,X3),c_union(X4,X2,X3),tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
c_union(v_X,v_Z,t_a) = v_X,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
( c_union(v_Y,v_Z,t_a) = v_X
| c_lessequals(v_X,c_union(v_Y,X1,t_a),tc_set(t_a))
| ~ c_lessequals(v_Z,c_union(v_Y,X1,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),v_X,t_a),X1,t_a)
| c_lessequals(c_union(X1,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_Y,v_X,tc_set(t_a)) ),
cls_conjecture_0 ).
cnf(c_0_38,negated_conjecture,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
cls_conjecture_3 ).
cnf(c_0_39,negated_conjecture,
( c_union(v_Y,v_Z,t_a) = v_X
| c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_40,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),v_X,t_a),X2,t_a)
| c_lessequals(c_union(X1,v_Z,t_a),v_X,tc_set(t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_24])]) ).
cnf(c_0_43,negated_conjecture,
( c_union(v_Y,v_Z,t_a) = v_X
| ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_16]) ).
cnf(c_0_45,negated_conjecture,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
cls_conjecture_2 ).
cnf(c_0_46,negated_conjecture,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) != v_X ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_41])]) ).
cnf(c_0_47,negated_conjecture,
c_union(v_Y,v_Z,t_a) = v_X,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_48,negated_conjecture,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_24])]) ).
cnf(c_0_49,negated_conjecture,
c_lessequals(v_Z,v_x,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_50,negated_conjecture,
( ~ c_lessequals(v_X,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
cls_conjecture_4 ).
cnf(c_0_51,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,c_union(X1,v_Z,t_a),t_a),v_Y,t_a)
| c_lessequals(v_X,c_union(X1,v_Z,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) != v_X ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_41])]) ).
cnf(c_0_53,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),X1,t_a),v_x,t_a)
| c_lessequals(c_union(X1,v_Z,t_a),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_X,v_x,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_24])]) ).
cnf(c_0_55,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,c_union(X1,v_Z,t_a),t_a),X2,t_a)
| c_lessequals(v_X,c_union(X1,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_Y,X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_19,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
c_lessequals(v_Y,v_x,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_47])]) ).
cnf(c_0_57,negated_conjecture,
c_lessequals(c_union(v_x,v_Z,t_a),v_x,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_16,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_41])]) ).
cnf(c_0_59,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,c_union(X1,v_Z,t_a),t_a),v_x,t_a)
| c_lessequals(v_X,c_union(X1,v_Z,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
c_union(v_x,v_Z,t_a) = v_x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_57]),c_0_31])]) ).
cnf(c_0_61,negated_conjecture,
~ c_lessequals(v_X,v_x,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_47])]) ).
cnf(c_0_62,negated_conjecture,
c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_x,t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_62]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET837-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.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 08:39:07 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 0.93/0.98 % Version : CSE_E---1.5
% 0.93/0.98 % Problem : theBenchmark.p
% 0.93/0.98 % Proof found
% 0.93/0.98 % SZS status Theorem for theBenchmark.p
% 0.93/0.98 % SZS output start Proof
% See solution above
% 0.93/0.99 % Total time : 0.441000 s
% 0.93/0.99 % SZS output end Proof
% 0.93/0.99 % Total time : 0.443000 s
%------------------------------------------------------------------------------