TSTP Solution File: ANA003-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA003-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 17:13:46 EDT 2023
% Result : Unsatisfiable 59.13s 59.20s
% Output : CNFRefutation 59.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 74 ( 8 unt; 16 typ; 0 def)
% Number of atoms : 151 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 205 ( 112 ~; 93 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 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 : 91 ( 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(add(absolute(add(f(fp33(X1)),minus(l1))),absolute(add(g(fp33(X1)),minus(l2)))),b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
cnf(axiom_6_1,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/ANA001-0.ax',axiom_6_1) ).
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/sandbox/benchmark/theBenchmark.p',c_13) ).
cnf(axiom_3,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/ANA001-0.ax',axiom_3) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',c_15) ).
cnf(left_identity,axiom,
add(n0,X1) = X1,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/ANA001-0.ax',axiom_6_2) ).
cnf(c_14,negated_conjecture,
less_than(n0,b),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',c_10) ).
cnf(c_12,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
cnf(c_0_15,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(add(absolute(add(f(fp33(X1)),minus(l1))),absolute(add(g(fp33(X1)),minus(l2)))),b) ),
c_16 ).
cnf(c_0_16,axiom,
add(X1,X2) = add(X2,X1),
axiom_6_1 ).
cnf(c_0_17,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_18,negated_conjecture,
( ~ less_than(add(absolute(add(minus(l1),f(fp33(X1)))),absolute(add(minus(l2),g(fp33(X1))))),b)
| ~ less_than(n0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_19,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
axiom_3 ).
cnf(c_0_20,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_17,c_0_16]) ).
cnf(c_0_21,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_22,axiom,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
transitivity_of_less_than ).
cnf(c_0_23,negated_conjecture,
( less_than(absolute(add(fp33(X1),minus(a))),X1)
| ~ less_than(n0,X1) ),
c_15 ).
cnf(c_0_24,negated_conjecture,
( ~ less_than(absolute(add(minus(l2),g(fp33(X1)))),half(b))
| ~ less_than(absolute(add(minus(l1),f(fp33(X1)))),half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,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_20,c_0_16]) ).
cnf(c_0_26,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_21,c_0_16]) ).
cnf(c_0_27,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_22,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( less_than(absolute(add(minus(a),fp33(X1))),X1)
| ~ less_than(n0,X1) ),
inference(rw,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_29,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_24,c_0_25]) ).
cnf(c_0_30,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_26,c_0_16]) ).
cnf(c_0_31,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_27,c_0_28]) ).
cnf(c_0_32,axiom,
add(n0,X1) = X1,
left_identity ).
cnf(c_0_33,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_29,c_0_30]) ).
cnf(c_0_34,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_31,c_0_32]),c_0_22]) ).
cnf(c_0_35,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_33,c_0_34]) ).
cnf(c_0_36,axiom,
( less_than(minimum(X1,X2),X1)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_2 ).
cnf(c_0_37,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_35,c_0_34]) ).
cnf(c_0_38,axiom,
( less_than(n0,half(X1))
| ~ less_than(n0,X1) ),
axiom_6_2 ).
cnf(c_0_39,negated_conjecture,
less_than(n0,b),
c_14 ).
cnf(c_0_40,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_27,c_0_36]) ).
cnf(c_0_41,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_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,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_40,c_0_32]),c_0_22]) ).
cnf(c_0_43,axiom,
( less_than(n0,minimum(X1,X2))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_1 ).
cnf(c_0_44,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_41,c_0_42]),c_0_43]) ).
cnf(c_0_45,axiom,
( less_than(minimum(X1,X2),X2)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_3 ).
cnf(c_0_46,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_44,c_0_45]) ).
cnf(c_0_47,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_46,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( less_than(n0,fp31(X1))
| ~ less_than(n0,X1) ),
c_10 ).
cnf(c_0_49,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_47,c_0_48]) ).
cnf(c_0_50,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_49,c_0_38]),c_0_39])]) ).
cnf(c_0_51,negated_conjecture,
( ~ less_than(n0,half(half(fp32(half(b)))))
| ~ less_than(n0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( ~ less_than(n0,half(fp32(half(b))))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_38]) ).
cnf(c_0_53,negated_conjecture,
( ~ less_than(n0,fp32(half(b)))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_38]) ).
cnf(c_0_54,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
c_12 ).
cnf(c_0_55,negated_conjecture,
( ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
~ less_than(n0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_38]),c_0_39])]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_39,c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:22:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 59.13/59.20 % Version : CSE_E---1.5
% 59.13/59.20 % Problem : theBenchmark.p
% 59.13/59.20 % Proof found
% 59.13/59.20 % SZS status Theorem for theBenchmark.p
% 59.13/59.20 % SZS output start Proof
% See solution above
% 59.13/59.21 % Total time : 58.605000 s
% 59.13/59.21 % SZS output end Proof
% 59.13/59.21 % Total time : 58.611000 s
%------------------------------------------------------------------------------