TSTP Solution File: HEN010-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN010-2 : 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 : n026.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 01:54:25 EDT 2023
% Result : Unsatisfiable 1.15s 1.19s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 48 ( 18 unt; 9 typ; 0 def)
% Number of atoms : 84 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 47 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 6 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,
a: $i ).
tff(decl_28,type,
idQa: $i ).
tff(decl_29,type,
idQ_idQa: $i ).
tff(decl_30,type,
idQa_Q__idQ_idQa: $i ).
cnf(one_inversion_equals_three,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
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(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X1,X1,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
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(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(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
cnf(c_0_13,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
one_inversion_equals_three ).
cnf(c_0_14,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_15,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_16,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
identity_divide_idQ_idQa ).
cnf(c_0_17,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_18,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_19,plain,
( X1 = divide(identity,X2)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_21,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_22,hypothesis,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,zero)
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X3,X5) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
quotient(X1,X1,zero),
x_divide_x_is_zero ).
cnf(c_0_25,hypothesis,
( divide(identity,idQ_idQa) = idQa
| ~ quotient(identity,X1,idQa) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_27,hypothesis,
( less_equal(X1,idQa)
| ~ less_equal(X1,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_29,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,hypothesis,
divide(identity,idQ_idQa) = idQa,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_32,hypothesis,
( less_equal(X1,idQa)
| ~ quotient(X1,idQa_Q__idQ_idQa,zero) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,hypothesis,
( less_equal(X1,idQa_Q__idQ_idQa)
| ~ quotient(X2,idQ_idQa,idQa)
| ~ quotient(X2,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_34,hypothesis,
quotient(identity,idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_35,hypothesis,
( idQa = X1
| ~ quotient(X1,idQa_Q__idQ_idQa,zero)
| ~ less_equal(idQa,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
( less_equal(X1,idQa_Q__idQ_idQa)
| ~ quotient(identity,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
prove_idQa_equals_idQa_Q__idQ_idQa ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24]),c_0_34])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN010-2 : 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 : n026.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 : Thu Aug 24 13:50:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.58 start to proof: theBenchmark
% 1.15/1.19 % Version : CSE_E---1.5
% 1.15/1.19 % Problem : theBenchmark.p
% 1.15/1.19 % Proof found
% 1.15/1.19 % SZS status Theorem for theBenchmark.p
% 1.15/1.19 % SZS output start Proof
% See solution above
% 1.15/1.20 % Total time : 0.605000 s
% 1.15/1.20 % SZS output end Proof
% 1.15/1.20 % Total time : 0.608000 s
%------------------------------------------------------------------------------