TSTP Solution File: LCL060-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL060-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 06:52:01 EDT 2023
% Result : Unsatisfiable 185.47s 185.33s
% Output : CNFRefutation 185.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 75 unt; 7 typ; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 206 ( 53 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
implies: ( $i * $i ) > $i ).
tff(decl_24,type,
is_a_theorem: $i > $i ).
tff(decl_25,type,
true: $i ).
tff(decl_26,type,
not: $i > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
cnf(condensed_detachment,axiom,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
cnf(prove_cn_54,negated_conjecture,
is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_54) ).
cnf(c_0_6,axiom,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
condensed_detachment ).
cnf(c_0_7,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
cn_1 ).
cnf(c_0_8,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_9,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)) = true,
cn_2 ).
cnf(c_0_10,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_11,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))) = true,
cn_3 ).
cnf(c_0_12,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_8]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]) ).
cnf(c_0_14,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(not(X1),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_8]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_8]) ).
cnf(c_0_16,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_17,plain,
is_a_theorem(implies(not(implies(X1,X1)),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_8]) ).
cnf(c_0_18,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(not(X1),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_8]) ).
cnf(c_0_19,plain,
ifeq(is_a_theorem(implies(implies(not(X1),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_8]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,X3)),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_8]) ).
cnf(c_0_21,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_8]) ).
cnf(c_0_22,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(not(X3),X2)),X4),implies(X3,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_8]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_8]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X2)),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_8]) ).
cnf(c_0_25,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X1),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_8]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X2),X3),implies(implies(X1,X2),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_23]),c_0_8]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_8]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(implies(implies(X1,implies(not(X2),X3)),X4),implies(X2,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_25]),c_0_8]) ).
cnf(c_0_29,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(X1),X1),X2),X3),implies(implies(X1,X2),X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_26]),c_0_8]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_7]),c_0_8]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(X1,implies(X2,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_27]),c_0_8]) ).
cnf(c_0_32,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(not(X2),X3)),X4)),true,is_a_theorem(implies(X2,X4)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_28]),c_0_8]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(implies(X2,X3),implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_8]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_31]),c_0_8]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_8]) ).
cnf(c_0_36,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(implies(X3,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_34]),c_0_8]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(X1,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_35]),c_0_8]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_8]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,X4),X2),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_34]),c_0_8]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(not(X1),implies(X1,implies(X2,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_37]),c_0_8]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X3,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_38]),c_0_8]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_39]),c_0_8]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(not(X1),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_40]),c_0_8]) ).
cnf(c_0_44,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X3,X2)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_41]),c_0_8]) ).
cnf(c_0_45,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X1),X2),X2),X3)),true,is_a_theorem(X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_42]),c_0_8]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X3),X4),implies(implies(implies(implies(not(X1),X1),X2),X3),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_26]),c_0_8]) ).
cnf(c_0_47,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(not(X1),X4)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_43]),c_0_8]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X3,implies(X1,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_8]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_8]) ).
cnf(c_0_50,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),X4)),true,is_a_theorem(implies(implies(X3,X1),X4)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_30]),c_0_8]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_8]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(not(X1),implies(X2,implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_8]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_49]),c_0_8]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_8]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(not(X2),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_52]),c_0_8]) ).
cnf(c_0_56,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_53]),c_0_8]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_54]),c_0_8]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_55]),c_0_8]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_8]) ).
cnf(c_0_60,plain,
ifeq(is_a_theorem(implies(implies(not(X1),implies(X1,X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_58]),c_0_8]) ).
cnf(c_0_61,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(implies(X1,X2),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_59]),c_0_8]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_8]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X1),X1),X3),X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_8]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_59]),c_0_8]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,X3),X2)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_63]),c_0_8]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_64]),c_0_8]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_65]),c_0_8]) ).
cnf(c_0_68,plain,
ifeq(is_a_theorem(implies(X1,implies(X2,X3))),true,is_a_theorem(implies(X2,implies(X1,X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_66]),c_0_8]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X1,X3),X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_67]),c_0_8]) ).
cnf(c_0_70,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X2),X3)),true,is_a_theorem(implies(implies(X1,X2),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_26]),c_0_8]) ).
cnf(c_0_71,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X1,X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_8]) ).
cnf(c_0_72,negated_conjecture,
is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))) != true,
prove_cn_54 ).
cnf(c_0_73,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_8]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL060-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n027.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 : Thu Aug 24 19:40:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 start to proof: theBenchmark
% 185.47/185.33 % Version : CSE_E---1.5
% 185.47/185.33 % Problem : theBenchmark.p
% 185.47/185.33 % Proof found
% 185.47/185.33 % SZS status Theorem for theBenchmark.p
% 185.47/185.33 % SZS output start Proof
% See solution above
% 185.47/185.34 % Total time : 184.718000 s
% 185.47/185.34 % SZS output end Proof
% 185.47/185.34 % Total time : 184.729000 s
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