TSTP Solution File: LAT274-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT274-2 : 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 : n025.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 06:00:24 EDT 2023
% Result : Unsatisfiable 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 34
% Syntax : Number of formulae : 73 ( 14 unt; 19 typ; 0 def)
% Number of atoms : 159 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 174 ( 69 ~; 105 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 10 >; 20 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 118 ( 19 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
t_a: $i ).
tff(decl_23,type,
tc_set: $i > $i ).
tff(decl_24,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
v_r: $i ).
tff(decl_27,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_28,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
v_sko__4mj: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
v_sko__4mk: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_emptyset: $i ).
tff(decl_32,type,
c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
v_cl: $i ).
tff(decl_34,type,
c_Tarski_OisLub: ( $i * $i * $i * $i ) > $o ).
tff(decl_35,type,
v_A: $i ).
tff(decl_36,type,
v_sko__4mi: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
v_b: $i ).
tff(decl_38,type,
v_S: $i ).
tff(decl_39,type,
v_a: $i ).
tff(decl_40,type,
v_L: $i ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(X1,X6,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Tarski_Ointerval(X4,X5,X6,X3),tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X1,v_cl,X2,t_a)
| ~ c_in(X3,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(X1,v_r,X3),X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(X1,v_r,X3),X1,t_a)
| ~ c_Tarski_OisLub(X1,v_cl,X2,t_a)
| ~ c_in(X3,v_A,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(cls_conjecture_4,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(X3,X4,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X1,X3,v_r),X1,t_a)
| c_in(v_sko__4mk(X4,X1,v_r),X1,t_a)
| X1 = c_emptyset
| ~ c_lessequals(X1,X2,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(cls_conjecture_3,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(X5,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Tarski_Ointerval(X4,X5,X6,X3),tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0,axiom,
( c_in(X1,c_Tarski_Ointerval(X4,X5,X2,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X1,X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2,axiom,
( c_in(c_Pair(X1,X4,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X4,X2,v_r),X2,t_a)
| X2 = c_emptyset
| ~ c_in(c_Pair(X1,v_sko__4mj(X2,X1,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,X3,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( c_in(c_Pair(X3,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X1,v_cl,X2,t_a)
| ~ c_in(X3,X1,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( c_in(c_Pair(X4,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X2,X4,v_r),X2,t_a)
| X2 = c_emptyset
| ~ c_in(c_Pair(v_sko__4mk(X1,X2,v_r),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,X3,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3,axiom,
( c_in(c_Pair(X1,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| X2 = c_emptyset
| ~ c_in(c_Pair(X1,v_sko__4mj(X2,X1,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X3,X2,v_r),X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,X4,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3) ).
cnf(c_0_15,axiom,
( c_in(c_Pair(X1,X6,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Tarski_Ointerval(X4,X5,X6,X3),tc_set(X3)) ),
cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_16,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
cls_conjecture_2 ).
cnf(c_0_17,axiom,
( c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X1,v_cl,X2,t_a)
| ~ c_in(X3,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(X1,v_r,X3),X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1 ).
cnf(c_0_18,negated_conjecture,
( c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
c_in(v_b,v_A,t_a),
cls_conjecture_1 ).
cnf(c_0_20,axiom,
( c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(X1,v_r,X3),X1,t_a)
| ~ c_Tarski_OisLub(X1,v_cl,X2,t_a)
| ~ c_in(X3,v_A,t_a) ),
cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_21,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
cls_conjecture_4 ).
cnf(c_0_22,axiom,
( c_in(c_Pair(X3,X4,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X1,X3,v_r),X1,t_a)
| c_in(v_sko__4mk(X4,X1,v_r),X1,t_a)
| X1 = c_emptyset
| ~ c_lessequals(X1,X2,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_23,negated_conjecture,
v_S != c_emptyset,
cls_conjecture_3 ).
cnf(c_0_24,negated_conjecture,
( c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X2,v_cl,X1,t_a)
| ~ c_in(v_sko__4mi(X2,v_r,v_b),v_S,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_25,negated_conjecture,
( c_in(c_Pair(v_L,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,X1),v_S,t_a)
| ~ c_in(X1,v_A,t_a) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,axiom,
( c_in(c_Pair(X5,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Tarski_Ointerval(X4,X5,X6,X3),tc_set(X3)) ),
cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_27,axiom,
( c_in(X1,c_Tarski_Ointerval(X4,X5,X2,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X1,X3,X3),X4,tc_prod(X3,X3)) ),
cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0 ).
cnf(c_0_28,negated_conjecture,
( c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X2,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,X1,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19])]) ).
cnf(c_0_30,axiom,
( c_in(c_Pair(X1,X4,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X4,X2,v_r),X2,t_a)
| X2 = c_emptyset
| ~ c_in(c_Pair(X1,v_sko__4mj(X2,X1,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,X3,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2 ).
cnf(c_0_31,negated_conjecture,
( c_in(c_Pair(v_a,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_32,negated_conjecture,
( c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a)
| c_in(v_sko__4mk(X2,v_S,v_r),v_S,t_a)
| c_in(X2,c_Tarski_Ointerval(v_r,X1,X3,t_a),t_a)
| ~ c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
( X1 = c_emptyset
| c_in(c_Pair(v_a,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X2,X1,v_r),X1,t_a)
| ~ c_in(v_sko__4mj(X1,v_a,v_r),v_S,t_a)
| ~ c_lessequals(X1,X3,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( c_in(v_L,c_Tarski_Ointerval(v_r,X1,v_b,t_a),t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
cls_conjecture_6 ).
cnf(c_0_37,negated_conjecture,
( c_in(c_Pair(v_a,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| ~ c_lessequals(v_S,X2,tc_set(t_a)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_23]),c_0_36]) ).
cnf(c_0_38,axiom,
( c_in(c_Pair(X3,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X1,v_cl,X2,t_a)
| ~ c_in(X3,X1,t_a) ),
cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0 ).
cnf(c_0_39,negated_conjecture,
( c_in(c_Pair(v_a,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a) ),
inference(spm,[status(thm)],[c_0_37,c_0_16]) ).
cnf(c_0_40,axiom,
( c_in(c_Pair(X4,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X2,X4,v_r),X2,t_a)
| X2 = c_emptyset
| ~ c_in(c_Pair(v_sko__4mk(X1,X2,v_r),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,X3,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1 ).
cnf(c_0_41,negated_conjecture,
( c_in(c_Pair(X1,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X1,v_S,t_a) ),
inference(spm,[status(thm)],[c_0_38,c_0_21]) ).
cnf(c_0_42,negated_conjecture,
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(X1,c_Tarski_Ointerval(v_r,v_a,X2,t_a),t_a)
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| ~ c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_43,axiom,
( c_in(c_Pair(X1,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| X2 = c_emptyset
| ~ c_in(c_Pair(X1,v_sko__4mj(X2,X1,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X3,X2,v_r),X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X2,X4,tc_set(t_a)) ),
cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3 ).
cnf(c_0_44,negated_conjecture,
( X1 = c_emptyset
| c_in(c_Pair(X2,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X1,X2,v_r),X1,t_a)
| ~ c_in(v_sko__4mk(v_L,X1,v_r),v_S,t_a)
| ~ c_lessequals(X1,X3,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_33]),c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( X1 = c_emptyset
| c_in(c_Pair(v_a,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X2,X1,v_r),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mj(X1,v_a,v_r),v_S,t_a)
| ~ c_lessequals(X1,X3,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_47,negated_conjecture,
( c_in(c_Pair(X1,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a)
| ~ c_lessequals(v_S,X2,tc_set(t_a)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_23]) ).
cnf(c_0_48,negated_conjecture,
( X1 = c_emptyset
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mj(X1,v_a,v_r),v_S,t_a)
| ~ c_in(v_sko__4mk(v_L,X1,v_r),v_S,t_a)
| ~ c_lessequals(X1,X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_46,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( c_in(c_Pair(X1,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a) ),
inference(spm,[status(thm)],[c_0_47,c_0_16]) ).
cnf(c_0_50,negated_conjecture,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X1,tc_set(t_a)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45])]),c_0_23]) ).
cnf(c_0_51,negated_conjecture,
c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_50,c_0_16]) ).
cnf(c_0_52,negated_conjecture,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,X1,t_a),t_a)
| ~ c_in(c_Pair(v_L,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_52]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT274-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.35 % Computer : n025.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 09:07:36 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.20/0.69 % Version : CSE_E---1.5
% 0.20/0.69 % Problem : theBenchmark.p
% 0.20/0.69 % Proof found
% 0.20/0.69 % SZS status Theorem for theBenchmark.p
% 0.20/0.69 % SZS output start Proof
% See solution above
% 0.20/0.70 % Total time : 0.101000 s
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70 % Total time : 0.104000 s
%------------------------------------------------------------------------------