TSTP Solution File: LCL278-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL278-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 06:53:22 EDT 2023
% Result : Unsatisfiable 79.04s 79.18s
% Output : CNFRefutation 79.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 96 ( 35 unt; 10 typ; 0 def)
% Number of atoms : 155 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 147 ( 78 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 173 ( 24 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
or: ( $i * $i ) > $i ).
tff(decl_23,type,
implies: ( $i * $i ) > $i ).
tff(decl_24,type,
axiom: $i > $o ).
tff(decl_25,type,
not: $i > $i ).
tff(decl_26,type,
theorem: $i > $o ).
tff(decl_27,type,
and: ( $i * $i ) > $i ).
tff(decl_28,type,
equivalent: ( $i * $i ) > $i ).
tff(decl_29,type,
p: $i ).
tff(decl_30,type,
q: $i ).
tff(decl_31,type,
r: $i ).
cnf(rule_2,axiom,
( theorem(X1)
| ~ theorem(implies(X2,X1))
| ~ theorem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_2) ).
cnf(implies_definition,axiom,
implies(X1,X2) = or(not(X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
cnf(rule_1,axiom,
( theorem(X1)
| ~ axiom(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).
cnf(axiom_1_3,axiom,
axiom(implies(X1,or(X2,X1))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
cnf(axiom_1_2,axiom,
axiom(implies(or(X1,X1),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
cnf(equivalent_defn,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).
cnf(and_defn,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-1.ax',and_defn) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(equivalent(p,q),equivalent(or(p,r),or(q,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_11,axiom,
( theorem(X1)
| ~ theorem(implies(X2,X1))
| ~ theorem(X2) ),
rule_2 ).
cnf(c_0_12,axiom,
implies(X1,X2) = or(not(X1),X2),
implies_definition ).
cnf(c_0_13,plain,
( theorem(X1)
| ~ theorem(X2)
| ~ theorem(or(not(X2),X1)) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
( theorem(X1)
| ~ axiom(X1) ),
rule_1 ).
cnf(c_0_15,axiom,
axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
axiom_1_6 ).
cnf(c_0_16,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
axiom_1_4 ).
cnf(c_0_17,axiom,
axiom(implies(X1,or(X2,X1))),
axiom_1_3 ).
cnf(c_0_18,plain,
( theorem(X1)
| ~ theorem(X2)
| ~ axiom(or(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_20,plain,
axiom(or(not(or(X1,X2)),or(X2,X1))),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_21,plain,
axiom(or(not(X1),or(X2,X1))),
inference(rw,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_22,plain,
( theorem(or(not(or(X1,X2)),or(X1,X3)))
| ~ theorem(or(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,plain,
( theorem(or(X1,X2))
| ~ theorem(X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_25,plain,
( theorem(or(X1,X2))
| ~ theorem(or(not(X3),X2))
| ~ theorem(or(X1,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_26,plain,
( theorem(or(X1,X2))
| ~ theorem(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X1,X3))
| ~ theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
( theorem(or(X1,X2))
| ~ axiom(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_29,axiom,
axiom(implies(or(X1,X1),X1)),
axiom_1_2 ).
cnf(c_0_30,plain,
( theorem(or(X1,X2))
| ~ theorem(not(X3))
| ~ axiom(or(X1,X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_31,plain,
( theorem(X1)
| ~ theorem(X2)
| ~ axiom(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_32,plain,
axiom(or(not(or(X1,X1)),X1)),
inference(rw,[status(thm)],[c_0_29,c_0_12]) ).
cnf(c_0_33,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X1,X3))
| ~ axiom(or(not(X3),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_34,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
axiom_1_5 ).
cnf(c_0_35,plain,
( theorem(or(not(X1),X2))
| ~ theorem(not(or(X3,X1))) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_36,plain,
( theorem(not(or(not(X1),not(X1))))
| ~ theorem(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_38,plain,
axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
inference(rw,[status(thm)],[c_0_34,c_0_12]) ).
cnf(c_0_39,plain,
( theorem(or(X1,X2))
| ~ theorem(not(X3))
| ~ axiom(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_40,plain,
( theorem(X1)
| ~ theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_41,plain,
( theorem(or(not(not(X1)),X2))
| ~ theorem(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( theorem(or(X1,X2))
| ~ axiom(or(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_43,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_38]) ).
cnf(c_0_44,plain,
( theorem(or(X1,X2))
| ~ theorem(not(not(or(X1,X1)))) ),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_45,plain,
( theorem(not(not(X1)))
| ~ theorem(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_47,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X1,X3)) ),
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_48,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
( theorem(or(X1,or(X2,X3)))
| ~ axiom(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_43,c_0_14]) ).
cnf(c_0_50,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
equivalent_defn ).
cnf(c_0_51,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_defn ).
cnf(c_0_52,plain,
theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_53,plain,
( theorem(or(not(or(X1,X2)),X1))
| ~ theorem(or(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_54,plain,
( theorem(or(X1,X2))
| ~ theorem(or(not(X3),X2))
| ~ theorem(X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_47]) ).
cnf(c_0_55,plain,
( theorem(or(or(X1,X2),X3))
| ~ axiom(or(X1,or(or(X1,X2),X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
~ theorem(implies(equivalent(p,q),equivalent(or(p,r),or(q,r)))),
prove_this ).
cnf(c_0_57,plain,
equivalent(X1,X2) = not(or(not(or(not(X1),X2)),not(or(not(X2),X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_12]),c_0_12]),c_0_51]) ).
cnf(c_0_58,plain,
( theorem(or(X1,not(not(X2))))
| ~ theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_59,plain,
( theorem(or(X1,or(not(or(X1,X2)),X3)))
| ~ theorem(or(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_60,plain,
( theorem(X1)
| ~ theorem(or(not(X2),X1))
| ~ theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_53]) ).
cnf(c_0_61,plain,
( theorem(or(X1,X2))
| ~ theorem(X3)
| ~ axiom(or(not(X3),X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_14]) ).
cnf(c_0_62,plain,
theorem(or(or(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_55,c_0_21]) ).
cnf(c_0_63,negated_conjecture,
~ theorem(or(not(not(or(not(or(not(p),q)),not(or(not(q),p))))),not(or(not(or(not(or(p,r)),or(q,r))),not(or(not(or(q,r)),or(p,r))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_12]),c_0_57]),c_0_57]) ).
cnf(c_0_64,plain,
( theorem(or(not(not(X1)),X2))
| ~ theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_58]) ).
cnf(c_0_65,plain,
( theorem(or(X1,or(not(or(not(X2),X3)),X4)))
| ~ theorem(or(not(X3),X4))
| ~ theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_59]) ).
cnf(c_0_66,plain,
( theorem(X1)
| ~ theorem(or(X1,or(X1,X2)))
| ~ theorem(or(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_53]) ).
cnf(c_0_67,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X3,X2)) ),
inference(spm,[status(thm)],[c_0_61,c_0_20]) ).
cnf(c_0_68,plain,
theorem(or(X1,or(not(X2),X2))),
inference(spm,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_69,negated_conjecture,
~ theorem(or(not(or(not(or(not(or(p,r)),or(q,r))),not(or(not(or(q,r)),or(p,r))))),or(not(or(not(p),q)),not(or(not(q),p))))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
( theorem(or(not(or(not(X1),X2)),or(X3,X4)))
| ~ theorem(or(not(X2),X4))
| ~ theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_65]) ).
cnf(c_0_71,plain,
( theorem(X1)
| ~ theorem(or(not(X2),X1))
| ~ theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
theorem(or(not(X1),or(X2,X1))),
inference(spm,[status(thm)],[c_0_43,c_0_68]) ).
cnf(c_0_73,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X1,or(X3,X2))) ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_74,negated_conjecture,
( ~ theorem(or(not(not(or(not(or(q,r)),or(p,r)))),not(or(not(q),p))))
| ~ theorem(or(not(or(not(p),q)),or(not(or(p,r)),or(q,r)))) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X2,or(X1,X2))) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
( theorem(or(X1,or(X2,or(X3,X4))))
| ~ theorem(or(X1,or(X3,or(X2,X4)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_77,plain,
theorem(or(not(X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( ~ theorem(or(not(or(not(p),q)),or(not(or(p,r)),or(q,r))))
| ~ theorem(or(not(or(not(q),p)),or(not(or(q,r)),or(p,r)))) ),
inference(spm,[status(thm)],[c_0_74,c_0_64]) ).
cnf(c_0_79,plain,
( theorem(or(not(or(not(X1),X2)),X3))
| ~ theorem(or(not(X2),X3))
| ~ theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_75,c_0_65]) ).
cnf(c_0_80,plain,
theorem(or(not(X1),or(X2,or(X1,X3)))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( ~ theorem(or(not(or(not(p),q)),or(not(or(p,r)),or(q,r))))
| ~ theorem(or(or(not(or(q,r)),or(p,r)),q)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_82,negated_conjecture,
( ~ theorem(or(or(not(or(q,r)),or(p,r)),q))
| ~ theorem(or(or(not(or(p,r)),or(q,r)),p)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_79]),c_0_80])]) ).
cnf(c_0_83,plain,
( theorem(or(or(not(or(X1,X2)),X3),X1))
| ~ theorem(or(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_59]) ).
cnf(c_0_84,negated_conjecture,
~ theorem(or(or(not(or(p,r)),or(q,r)),p)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_72])]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : LCL278-3 : TPTP v8.1.2. Released v2.3.0.
% 0.06/0.07 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.26 % Computer : n009.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Fri Aug 25 00:37:05 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.10/0.41 start to proof: theBenchmark
% 79.04/79.18 % Version : CSE_E---1.5
% 79.04/79.18 % Problem : theBenchmark.p
% 79.04/79.18 % Proof found
% 79.04/79.18 % SZS status Theorem for theBenchmark.p
% 79.04/79.18 % SZS output start Proof
% See solution above
% 79.04/79.18 % Total time : 78.764000 s
% 79.04/79.18 % SZS output end Proof
% 79.04/79.18 % Total time : 78.770000 s
%------------------------------------------------------------------------------