TSTP Solution File: ANA005-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 : Wed Aug 30 17:13:48 EDT 2023
% Result : Unsatisfiable 102.29s 102.33s
% Output : CNFRefutation 102.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 34
% Syntax : Number of formulae : 88 ( 15 unt; 16 typ; 0 def)
% Number of atoms : 175 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 227 ( 124 ~; 103 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 11 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 130 ( 5 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
n0: $i ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
less_than: ( $i * $i ) > $o ).
tff(decl_25,type,
minimum: ( $i * $i ) > $i ).
tff(decl_26,type,
half: $i > $i ).
tff(decl_27,type,
absolute: $i > $i ).
tff(decl_28,type,
minus: $i > $i ).
tff(decl_29,type,
fp31: $i > $i ).
tff(decl_30,type,
a: $i ).
tff(decl_31,type,
f: $i > $i ).
tff(decl_32,type,
l1: $i ).
tff(decl_33,type,
fp32: $i > $i ).
tff(decl_34,type,
g: $i > $i ).
tff(decl_35,type,
l2: $i ).
tff(decl_36,type,
b: $i ).
tff(decl_37,type,
fp33: $i > $i ).
cnf(c_16,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(absolute(add(add(f(fp33(X1)),g(fp33(X1))),minus(add(l1,l2)))),b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
cnf(axiom_5,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_5) ).
cnf(c_17,axiom,
( less_than(absolute(add(X1,X2)),X3)
| ~ less_than(add(absolute(X1),absolute(X2)),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',c_17) ).
cnf(axiom_3,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_3) ).
cnf(axiom_6_1,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_6_1) ).
cnf(axiom_8,axiom,
minus(add(X1,X2)) = add(minus(X1),minus(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_8) ).
cnf(c_13,negated_conjecture,
( less_than(absolute(add(g(X2),minus(l2))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp32(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
cnf(c_11,negated_conjecture,
( less_than(absolute(add(f(X2),minus(l1))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp31(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
cnf(transitivity_of_less_than,axiom,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',transitivity_of_less_than) ).
cnf(c_15,negated_conjecture,
( less_than(absolute(add(fp33(X1),minus(a))),X1)
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
cnf(left_identity,axiom,
add(n0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',left_identity) ).
cnf(axiom_2_2,axiom,
( less_than(minimum(X1,X2),X1)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_2_2) ).
cnf(axiom_6_2,axiom,
( less_than(n0,half(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_6_2) ).
cnf(c_14,negated_conjecture,
less_than(n0,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
cnf(axiom_2_1,axiom,
( less_than(n0,minimum(X1,X2))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_2_1) ).
cnf(axiom_2_3,axiom,
( less_than(minimum(X1,X2),X2)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_2_3) ).
cnf(c_10,negated_conjecture,
( less_than(n0,fp31(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
cnf(c_12,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
cnf(c_0_18,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(absolute(add(add(f(fp33(X1)),g(fp33(X1))),minus(add(l1,l2)))),b) ),
c_16 ).
cnf(c_0_19,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
axiom_5 ).
cnf(c_0_20,axiom,
( less_than(absolute(add(X1,X2)),X3)
| ~ less_than(add(absolute(X1),absolute(X2)),X3) ),
c_17 ).
cnf(c_0_21,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
axiom_3 ).
cnf(c_0_22,negated_conjecture,
( ~ less_than(absolute(add(f(fp33(X1)),add(g(fp33(X1)),minus(add(l1,l2))))),b)
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
add(X1,X2) = add(X2,X1),
axiom_6_1 ).
cnf(c_0_24,axiom,
minus(add(X1,X2)) = add(minus(X1),minus(X2)),
axiom_8 ).
cnf(c_0_25,plain,
( less_than(absolute(add(X1,X2)),X3)
| ~ less_than(absolute(X2),half(X3))
| ~ less_than(absolute(X1),half(X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( ~ less_than(absolute(add(f(fp33(X1)),add(minus(add(l1,l2)),g(fp33(X1))))),b)
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_28,plain,
add(minus(add(X1,X2)),X3) = add(minus(X1),add(minus(X2),X3)),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_29,plain,
( less_than(absolute(add(X1,add(X2,X3))),X4)
| ~ less_than(absolute(add(X1,X2)),half(X4))
| ~ less_than(absolute(X3),half(X4)) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_30,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_19]) ).
cnf(c_0_31,negated_conjecture,
( less_than(absolute(add(g(X2),minus(l2))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp32(X1)) ),
c_13 ).
cnf(c_0_32,negated_conjecture,
( ~ less_than(absolute(add(minus(l1),add(minus(l2),add(f(fp33(X1)),g(fp33(X1)))))),b)
| ~ less_than(n0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),c_0_28]) ).
cnf(c_0_33,plain,
( less_than(absolute(add(X1,add(X2,add(X3,X4)))),X5)
| ~ less_than(absolute(add(X1,X3)),half(X5))
| ~ less_than(absolute(add(X2,X4)),half(X5)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( less_than(absolute(add(minus(l2),g(X1))),X2)
| ~ less_than(absolute(add(X1,minus(a))),fp32(X2))
| ~ less_than(n0,X2) ),
inference(rw,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( less_than(absolute(add(f(X2),minus(l1))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp31(X1)) ),
c_11 ).
cnf(c_0_36,axiom,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
transitivity_of_less_than ).
cnf(c_0_37,negated_conjecture,
( less_than(absolute(add(fp33(X1),minus(a))),X1)
| ~ less_than(n0,X1) ),
c_15 ).
cnf(c_0_38,negated_conjecture,
( ~ less_than(absolute(add(minus(l1),f(fp33(X1)))),half(b))
| ~ less_than(absolute(add(minus(l2),g(fp33(X1)))),half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( less_than(absolute(add(minus(l2),g(X1))),X2)
| ~ less_than(absolute(add(minus(a),X1)),fp32(X2))
| ~ less_than(n0,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_40,negated_conjecture,
( less_than(absolute(add(minus(l1),f(X1))),X2)
| ~ less_than(absolute(add(X1,minus(a))),fp31(X2))
| ~ less_than(n0,X2) ),
inference(rw,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_41,plain,
( less_than(X1,X2)
| ~ less_than(X1,add(X3,X4))
| ~ less_than(X4,half(X2))
| ~ less_than(X3,half(X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_42,negated_conjecture,
( less_than(absolute(add(minus(a),fp33(X1))),X1)
| ~ less_than(n0,X1) ),
inference(rw,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_43,negated_conjecture,
( ~ less_than(absolute(add(minus(l1),f(fp33(X1)))),half(b))
| ~ less_than(absolute(add(minus(a),fp33(X1))),fp32(half(b)))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( less_than(absolute(add(minus(l1),f(X1))),X2)
| ~ less_than(absolute(add(minus(a),X1)),fp31(X2))
| ~ less_than(n0,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_45,negated_conjecture,
( less_than(absolute(add(minus(a),fp33(add(X1,X2)))),X3)
| ~ less_than(n0,add(X1,X2))
| ~ less_than(X2,half(X3))
| ~ less_than(X1,half(X3)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,axiom,
add(n0,X1) = X1,
left_identity ).
cnf(c_0_47,negated_conjecture,
( ~ less_than(absolute(add(minus(a),fp33(X1))),fp32(half(b)))
| ~ less_than(absolute(add(minus(a),fp33(X1))),fp31(half(b)))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( less_than(absolute(add(minus(a),fp33(X1))),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(n0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_36]) ).
cnf(c_0_49,negated_conjecture,
( ~ less_than(absolute(add(minus(a),fp33(X1))),fp31(half(b)))
| ~ less_than(X1,half(fp32(half(b))))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,axiom,
( less_than(minimum(X1,X2),X1)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_2 ).
cnf(c_0_51,negated_conjecture,
( ~ less_than(X1,half(fp32(half(b))))
| ~ less_than(X1,half(fp31(half(b))))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_52,axiom,
( less_than(n0,half(X1))
| ~ less_than(n0,X1) ),
axiom_6_2 ).
cnf(c_0_53,negated_conjecture,
less_than(n0,b),
c_14 ).
cnf(c_0_54,plain,
( less_than(minimum(add(X1,X2),X3),X4)
| ~ less_than(n0,add(X1,X2))
| ~ less_than(X2,half(X4))
| ~ less_than(X1,half(X4))
| ~ less_than(n0,X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( ~ less_than(X1,half(fp32(half(b))))
| ~ less_than(X1,half(fp31(half(b))))
| ~ less_than(n0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_56,plain,
( less_than(minimum(X1,X2),X3)
| ~ less_than(X1,half(X3))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_36]) ).
cnf(c_0_57,axiom,
( less_than(n0,minimum(X1,X2))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_1 ).
cnf(c_0_58,negated_conjecture,
( ~ less_than(minimum(X1,X2),half(fp31(half(b))))
| ~ less_than(X1,half(half(fp32(half(b)))))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_59,axiom,
( less_than(minimum(X1,X2),X2)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_3 ).
cnf(c_0_60,negated_conjecture,
( ~ less_than(X1,half(half(fp32(half(b)))))
| ~ less_than(n0,half(fp31(half(b))))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( ~ less_than(X1,half(half(fp32(half(b)))))
| ~ less_than(n0,fp31(half(b)))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( less_than(n0,fp31(X1))
| ~ less_than(n0,X1) ),
c_10 ).
cnf(c_0_63,negated_conjecture,
( ~ less_than(X1,half(half(fp32(half(b)))))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
( ~ less_than(X1,half(half(fp32(half(b)))))
| ~ less_than(n0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_53])]) ).
cnf(c_0_65,negated_conjecture,
( ~ less_than(n0,half(half(fp32(half(b)))))
| ~ less_than(n0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_50]),c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( ~ less_than(n0,half(fp32(half(b))))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_52]) ).
cnf(c_0_67,negated_conjecture,
( ~ less_than(n0,fp32(half(b)))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_52]) ).
cnf(c_0_68,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
c_12 ).
cnf(c_0_69,negated_conjecture,
( ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,negated_conjecture,
~ less_than(n0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_52]),c_0_53])]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_53,c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:47:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 102.29/102.33 % Version : CSE_E---1.5
% 102.29/102.33 % Problem : theBenchmark.p
% 102.29/102.33 % Proof found
% 102.29/102.33 % SZS status Theorem for theBenchmark.p
% 102.29/102.33 % SZS output start Proof
% See solution above
% 102.29/102.34 % Total time : 101.750000 s
% 102.29/102.34 % SZS output end Proof
% 102.29/102.34 % Total time : 101.758000 s
%------------------------------------------------------------------------------