TSTP Solution File: HEN007-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN007-1 : 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 : n016.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 01:54:20 EDT 2023
% Result : Unsatisfiable 3.73s 4.02s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 72 ( 32 unt; 10 typ; 0 def)
% Number of atoms : 120 ( 12 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 118 ( 60 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 114 ( 9 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
less_equal: ( $i * $i ) > $o ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
quotient: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
identity: $i ).
tff(decl_26,type,
divide: ( $i * $i ) > $i ).
tff(decl_27,type,
x: $i ).
tff(decl_28,type,
y: $i ).
tff(decl_29,type,
z: $i ).
tff(decl_30,type,
zQy: $i ).
tff(decl_31,type,
zQx: $i ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(zQx,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQx) ).
cnf(zQy,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQy) ).
cnf(xLEy,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
cnf(prove_zQyLEzQx,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
cnf(c_0_11,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_12,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_13,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property ).
cnf(c_0_14,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_15,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,X6))
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_20,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_21,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_22,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_23,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_24,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_26,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_27,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ quotient(X1,X2,zero) ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_29,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_12,c_0_27]) ).
cnf(c_0_30,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26])]) ).
cnf(c_0_31,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_12,c_0_30]) ).
cnf(c_0_32,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_33,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_34,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,divide(X2,zero),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_12]) ).
cnf(c_0_35,hypothesis,
quotient(z,x,zQx),
zQx ).
cnf(c_0_36,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_34,c_0_12]) ).
cnf(c_0_37,hypothesis,
less_equal(zQx,z),
inference(spm,[status(thm)],[c_0_11,c_0_35]) ).
cnf(c_0_38,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_36]),c_0_26])]) ).
cnf(c_0_39,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_40,hypothesis,
quotient(zQx,z,zero),
inference(spm,[status(thm)],[c_0_14,c_0_37]) ).
cnf(c_0_41,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_42,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(z,X3,X2)
| ~ quotient(zQx,X3,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,hypothesis,
quotient(z,y,zQy),
zQy ).
cnf(c_0_44,hypothesis,
less_equal(x,y),
xLEy ).
cnf(c_0_45,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_41]),c_0_26])]) ).
cnf(c_0_46,hypothesis,
( less_equal(divide(X1,zQy),zero)
| ~ quotient(zQx,y,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( less_equal(divide(X1,X2),divide(X3,X4))
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X5,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_48,hypothesis,
quotient(x,y,zero),
inference(spm,[status(thm)],[c_0_14,c_0_44]) ).
cnf(c_0_49,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_12,c_0_45]) ).
cnf(c_0_50,hypothesis,
( divide(X1,zQy) = zero
| ~ quotient(zQx,y,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_46]),c_0_26])]) ).
cnf(c_0_51,hypothesis,
( less_equal(divide(X1,zero),divide(X2,y))
| ~ quotient(X3,y,X1)
| ~ quotient(X3,x,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_49]),c_0_17])]) ).
cnf(c_0_53,hypothesis,
( quotient(X1,zQy,zero)
| ~ quotient(zQx,y,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_50]) ).
cnf(c_0_54,hypothesis,
( less_equal(X1,divide(X2,y))
| ~ quotient(X3,y,X1)
| ~ quotient(X3,x,X2) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,hypothesis,
quotient(divide(zQx,y),zQy,zero),
inference(spm,[status(thm)],[c_0_53,c_0_12]) ).
cnf(c_0_56,hypothesis,
( less_equal(zQy,divide(X1,y))
| ~ quotient(z,x,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_43]) ).
cnf(c_0_57,hypothesis,
( divide(zQx,y) = zQy
| ~ quotient(zQy,divide(zQx,y),zero) ),
inference(spm,[status(thm)],[c_0_28,c_0_55]) ).
cnf(c_0_58,hypothesis,
( quotient(zQy,divide(X1,y),zero)
| ~ quotient(z,x,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_56]) ).
cnf(c_0_59,hypothesis,
divide(zQx,y) = zQy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_35])]) ).
cnf(c_0_60,negated_conjecture,
~ less_equal(zQy,zQx),
prove_zQyLEzQx ).
cnf(c_0_61,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_59]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 24 13:58:24 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 3.73/4.02 % Version : CSE_E---1.5
% 3.73/4.02 % Problem : theBenchmark.p
% 3.73/4.02 % Proof found
% 3.73/4.02 % SZS status Theorem for theBenchmark.p
% 3.73/4.02 % SZS output start Proof
% See solution above
% 3.73/4.03 % Total time : 3.448000 s
% 3.73/4.03 % SZS output end Proof
% 3.73/4.03 % Total time : 3.451000 s
%------------------------------------------------------------------------------