TSTP Solution File: ANA004-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA004-1 : 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 : n002.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 17:13:47 EDT 2023
% Result : Unsatisfiable 72.92s 73.00s
% Output : CNFRefutation 72.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 33
% Syntax : Number of formulae : 80 ( 10 unt; 16 typ; 0 def)
% Number of atoms : 163 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 217 ( 118 ~; 99 |; 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 : 110 ( 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_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(c_16,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(absolute(add(add(f(fp33(X1)),minus(l1)),add(g(fp33(X1)),minus(l2)))),b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
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_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_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_17,axiom,
( less_than(absolute(add(X1,X2)),X3)
| ~ less_than(add(absolute(X1),absolute(X2)),X3) ),
c_17 ).
cnf(c_0_18,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
axiom_3 ).
cnf(c_0_19,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(absolute(add(add(f(fp33(X1)),minus(l1)),add(g(fp33(X1)),minus(l2)))),b) ),
c_16 ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
axiom_6_1 ).
cnf(c_0_21,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
axiom_5 ).
cnf(c_0_22,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_17,c_0_18]) ).
cnf(c_0_23,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_24,negated_conjecture,
( ~ less_than(absolute(add(minus(l1),add(f(fp33(X1)),add(minus(l2),g(fp33(X1)))))),b)
| ~ less_than(n0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]),c_0_21]) ).
cnf(c_0_25,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_22,c_0_21]) ).
cnf(c_0_26,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_23,c_0_20]) ).
cnf(c_0_27,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_28,axiom,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
transitivity_of_less_than ).
cnf(c_0_29,negated_conjecture,
( less_than(absolute(add(fp33(X1),minus(a))),X1)
| ~ less_than(n0,X1) ),
c_15 ).
cnf(c_0_30,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_24,c_0_25]) ).
cnf(c_0_31,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_26,c_0_20]) ).
cnf(c_0_32,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_27,c_0_20]) ).
cnf(c_0_33,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_28,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( less_than(absolute(add(minus(a),fp33(X1))),X1)
| ~ less_than(n0,X1) ),
inference(rw,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_35,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_30,c_0_31]) ).
cnf(c_0_36,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_32,c_0_20]) ).
cnf(c_0_37,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_33,c_0_34]) ).
cnf(c_0_38,axiom,
add(n0,X1) = X1,
left_identity ).
cnf(c_0_39,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_35,c_0_36]) ).
cnf(c_0_40,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_37,c_0_38]),c_0_28]) ).
cnf(c_0_41,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_39,c_0_40]) ).
cnf(c_0_42,axiom,
( less_than(minimum(X1,X2),X1)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_2 ).
cnf(c_0_43,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_41,c_0_40]) ).
cnf(c_0_44,axiom,
( less_than(n0,half(X1))
| ~ less_than(n0,X1) ),
axiom_6_2 ).
cnf(c_0_45,negated_conjecture,
less_than(n0,b),
c_14 ).
cnf(c_0_46,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_33,c_0_42]) ).
cnf(c_0_47,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_43,c_0_44]),c_0_45])]) ).
cnf(c_0_48,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_46,c_0_38]),c_0_28]) ).
cnf(c_0_49,axiom,
( less_than(n0,minimum(X1,X2))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_1 ).
cnf(c_0_50,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_47,c_0_48]),c_0_49]) ).
cnf(c_0_51,axiom,
( less_than(minimum(X1,X2),X2)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_3 ).
cnf(c_0_52,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_50,c_0_51]) ).
cnf(c_0_53,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_52,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( less_than(n0,fp31(X1))
| ~ less_than(n0,X1) ),
c_10 ).
cnf(c_0_55,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_53,c_0_54]) ).
cnf(c_0_56,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_55,c_0_44]),c_0_45])]) ).
cnf(c_0_57,negated_conjecture,
( ~ less_than(n0,half(half(fp32(half(b)))))
| ~ less_than(n0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_42]),c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( ~ less_than(n0,half(fp32(half(b))))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( ~ less_than(n0,fp32(half(b)))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_44]) ).
cnf(c_0_60,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
c_12 ).
cnf(c_0_61,negated_conjecture,
( ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,negated_conjecture,
~ less_than(n0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_44]),c_0_45])]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_45,c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 : Fri Aug 25 18:58:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 72.92/73.00 % Version : CSE_E---1.5
% 72.92/73.00 % Problem : theBenchmark.p
% 72.92/73.00 % Proof found
% 72.92/73.00 % SZS status Theorem for theBenchmark.p
% 72.92/73.00 % SZS output start Proof
% See solution above
% 72.92/73.00 % Total time : 72.458000 s
% 72.92/73.00 % SZS output end Proof
% 72.92/73.00 % Total time : 72.463000 s
%------------------------------------------------------------------------------