TSTP Solution File: LAT276-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT276-2 : 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 : n011.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 06:00:25 EDT 2023
% Result : Unsatisfiable 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 28
% Syntax : Number of formulae : 56 ( 9 unt; 16 typ; 0 def)
% Number of atoms : 93 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 49 ~; 53 |; 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 : 25 ( 9 >; 16 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_S: $i ).
tff(decl_23,type,
v_A: $i ).
tff(decl_24,type,
t_a: $i ).
tff(decl_25,type,
tc_set: $i > $i ).
tff(decl_26,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
v_xa: $i ).
tff(decl_28,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_29,type,
v_cl: $i ).
tff(decl_30,type,
tc_Product__Type_Ounit: $i ).
tff(decl_31,type,
c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_33,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
v_r: $i ).
tff(decl_37,type,
v_sko__4mP: ( $i * $i * $i ) > $i ).
cnf(cls_conjecture_10,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a)
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
cnf(cls_conjecture_9,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a)
| ~ c_in(X1,v_S,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(X1,c_Tarski_Olub(X2,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,X2,t_a)
| ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mP(X1,X2,v_r),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| c_in(v_xa,v_S,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(X1,X2,v_r),X2,t_a)
| ~ c_in(X1,v_A,t_a)
| ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(c_0_12,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a)
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
cls_conjecture_10 ).
cnf(c_0_13,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
cls_Tarski_Or_A_61_61_Aorder_Acl_0 ).
cnf(c_0_14,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a)
| ~ c_in(X1,v_S,t_a) ),
cls_conjecture_9 ).
cnf(c_0_15,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,axiom,
( c_in(c_Pair(X1,c_Tarski_Olub(X2,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,X2,t_a)
| ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_17,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
cls_conjecture_0 ).
cnf(c_0_18,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a)
| ~ c_in(X1,v_S,t_a) ),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
cls_conjecture_4 ).
cnf(c_0_20,axiom,
( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mP(X1,X2,v_r),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1 ).
cnf(c_0_21,negated_conjecture,
( c_in(c_Pair(X1,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| c_in(v_xa,v_S,t_a) ),
cls_conjecture_3 ).
cnf(c_0_23,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
cls_Tarski_OA_A_61_61_Apset_Acl_0 ).
cnf(c_0_24,negated_conjecture,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
cls_conjecture_6 ).
cnf(c_0_25,axiom,
( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(X1,X2,v_r),X2,t_a)
| ~ c_in(X1,v_A,t_a)
| ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_26,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rw,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( c_in(c_Pair(c_Tarski_Olub(X1,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mP(v_xa,X1,v_r),v_S,t_a)
| ~ c_in(v_xa,v_A,t_a)
| ~ c_lessequals(X1,v_A,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( c_in(v_xa,v_A,t_a)
| c_in(v_xa,v_S,t_a) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_13]),c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(X1,v_S,v_r),v_S,t_a)
| ~ c_in(X1,v_A,t_a) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_xa,v_A,t_a) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
c_in(v_xa,v_S,t_a),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_28]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| ~ c_in(v_xa,v_A,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_17])]),c_0_33])]) ).
cnf(c_0_35,negated_conjecture,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_xa,v_A,t_a) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_17])]),c_0_34]) ).
cnf(c_0_36,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_37,negated_conjecture,
~ c_in(v_xa,v_A,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_16]),c_0_33]),c_0_17])]) ).
cnf(c_0_38,negated_conjecture,
( c_in(X1,v_A,t_a)
| ~ c_in(X1,v_S,t_a) ),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT276-2 : 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 : n011.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 : Thu Aug 24 07:02:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.034000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.037000 s
%------------------------------------------------------------------------------