TSTP Solution File: HEN003-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN003-1 : 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 : n005.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 01:54:14 EDT 2023
% Result : Unsatisfiable 0.15s 0.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 36 ( 16 unt; 6 typ; 0 def)
% Number of atoms : 60 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 32 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 10 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 ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(prove_x_divide_x_is_zero,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
cnf(c_0_8,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_9,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_10,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_11,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_12,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,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_10,c_0_9]) ).
cnf(c_0_14,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_16,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_13,c_0_14]) ).
cnf(c_0_17,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_18,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,divide(X3,X4))
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( less_equal(divide(divide(X1,X2),zero),zero)
| ~ quotient(X1,zero,divide(X2,X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_20,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_21,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_19,c_0_9]) ).
cnf(c_0_22,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]) ).
cnf(c_0_23,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_24,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_9,c_0_22]) ).
cnf(c_0_25,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
~ quotient(x,x,zero),
prove_x_divide_x_is_zero ).
cnf(c_0_28,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_9,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : HEN003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Aug 24 13:25:38 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.53 start to proof: theBenchmark
% 0.15/0.55 % Version : CSE_E---1.5
% 0.15/0.55 % Problem : theBenchmark.p
% 0.15/0.55 % Proof found
% 0.15/0.55 % SZS status Theorem for theBenchmark.p
% 0.15/0.55 % SZS output start Proof
% See solution above
% 0.15/0.55 % Total time : 0.006000 s
% 0.15/0.55 % SZS output end Proof
% 0.15/0.55 % Total time : 0.008000 s
%------------------------------------------------------------------------------