TSTP Solution File: HAL006+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 01:53:28 EDT 2023
% Result : Theorem 1.66s 1.72s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 44
% Syntax : Number of formulae : 75 ( 14 unt; 37 typ; 0 def)
% Number of atoms : 100 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 35 |; 19 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 22 >; 34 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-6 aty)
% Number of variables : 61 ( 0 sgn; 30 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
morphism: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
element: ( $i * $i ) > $o ).
tff(decl_24,type,
apply: ( $i * $i ) > $i ).
tff(decl_25,type,
zero: $i > $i ).
tff(decl_26,type,
injection: $i > $o ).
tff(decl_27,type,
surjection: $i > $o ).
tff(decl_28,type,
exact: ( $i * $i ) > $o ).
tff(decl_29,type,
commute: ( $i * $i * $i * $i ) > $o ).
tff(decl_30,type,
subtract: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
alpha: $i ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
b: $i ).
tff(decl_34,type,
beta: $i ).
tff(decl_35,type,
c: $i ).
tff(decl_36,type,
gamma: $i ).
tff(decl_37,type,
d: $i ).
tff(decl_38,type,
e: $i ).
tff(decl_39,type,
delta: $i ).
tff(decl_40,type,
r: $i ).
tff(decl_41,type,
f: $i ).
tff(decl_42,type,
g: $i ).
tff(decl_43,type,
h: $i ).
tff(decl_44,type,
gammma: $i ).
tff(decl_45,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_48,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk5_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
esk6_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
esk7_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_52,type,
esk8_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
esk9_1: $i > $i ).
tff(decl_54,type,
esk10_1: $i > $i ).
tff(decl_55,type,
esk11_1: $i > $i ).
tff(decl_56,type,
esk12_1: $i > $i ).
tff(decl_57,type,
esk13_1: $i > $i ).
tff(decl_58,type,
esk14_0: $i ).
fof(lemma12,conjecture,
! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma12) ).
fof(morphism,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(lemma8,axiom,
! [X19] :
( element(X19,e)
=> ? [X21,X22,X23] :
( element(X21,b)
& element(X22,e)
& subtract(e,apply(g,X21),X19) = X22
& element(X23,a)
& apply(gamma,apply(f,X23)) = X22
& apply(g,apply(alpha,X23)) = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma8) ).
fof(subtract_distribution,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(alpha_morphism,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
fof(subtract_cancellation,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> subtract(X2,X5,subtract(X2,X5,X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
fof(c_0_7,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
inference(assume_negation,[status(cth)],[lemma12]) ).
fof(c_0_8,plain,
! [X25,X26,X27,X28] :
( ( ~ element(X28,X26)
| element(apply(X25,X28),X27)
| ~ morphism(X25,X26,X27) )
& ( apply(X25,zero(X26)) = zero(X27)
| ~ morphism(X25,X26,X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])]) ).
fof(c_0_9,plain,
! [X100] :
( ( element(esk11_1(X100),b)
| ~ element(X100,e) )
& ( element(esk12_1(X100),e)
| ~ element(X100,e) )
& ( subtract(e,apply(g,esk11_1(X100)),X100) = esk12_1(X100)
| ~ element(X100,e) )
& ( element(esk13_1(X100),a)
| ~ element(X100,e) )
& ( apply(gamma,apply(f,esk13_1(X100))) = esk12_1(X100)
| ~ element(X100,e) )
& ( apply(g,apply(alpha,esk13_1(X100))) = esk12_1(X100)
| ~ element(X100,e) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma8])])])]) ).
fof(c_0_10,negated_conjecture,
! [X105,X106] :
( element(esk14_0,e)
& ( ~ element(X105,b)
| ~ element(X106,b)
| apply(g,subtract(b,X105,X106)) != esk14_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X92,X93,X94,X95,X96] :
( ~ morphism(X92,X93,X94)
| ~ element(X95,X93)
| ~ element(X96,X93)
| apply(X92,subtract(X93,X95,X96)) = subtract(X94,apply(X92,X95),apply(X92,X96)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])]) ).
cnf(c_0_12,plain,
( element(apply(X3,X1),X4)
| ~ element(X1,X2)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
morphism(alpha,a,b),
inference(split_conjunct,[status(thm)],[alpha_morphism]) ).
cnf(c_0_14,plain,
( element(esk13_1(X1),a)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
element(esk14_0,e),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X89,X90,X91] :
( ~ element(X90,X89)
| ~ element(X91,X89)
| subtract(X89,X90,subtract(X89,X90,X91)) = X91 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).
cnf(c_0_17,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_18,plain,
( element(esk11_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5))
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| ~ element(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( element(apply(alpha,X1),b)
| ~ element(X1,a) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
element(esk13_1(esk14_0),a),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( apply(g,apply(alpha,esk13_1(X1))) = esk12_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,plain,
( subtract(X2,X1,subtract(X2,X1,X3)) = X3
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
element(esk11_1(esk14_0),b),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_26,plain,
( subtract(e,apply(g,esk11_1(X1)),X1) = esk12_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( apply(g,subtract(b,X1,X2)) = subtract(e,apply(g,X1),apply(g,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
element(apply(alpha,esk13_1(esk14_0)),b),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
apply(g,apply(alpha,esk13_1(esk14_0))) = esk12_1(esk14_0),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( subtract(e,X1,subtract(e,X1,esk14_0)) = esk14_0
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
element(apply(g,esk11_1(esk14_0)),e),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
subtract(e,apply(g,esk11_1(esk14_0)),esk14_0) = esk12_1(esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( apply(g,subtract(b,X1,apply(alpha,esk13_1(esk14_0)))) = subtract(e,apply(g,X1),esk12_1(esk14_0))
| ~ element(X1,b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
subtract(e,apply(g,esk11_1(esk14_0)),esk12_1(esk14_0)) = esk14_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( ~ element(X1,b)
| ~ element(X2,b)
| apply(g,subtract(b,X1,X2)) != esk14_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,negated_conjecture,
apply(g,subtract(b,esk11_1(esk14_0),apply(alpha,esk13_1(esk14_0)))) = esk14_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:48:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.66/1.72 % Version : CSE_E---1.5
% 1.66/1.72 % Problem : theBenchmark.p
% 1.66/1.72 % Proof found
% 1.66/1.72 % SZS status Theorem for theBenchmark.p
% 1.66/1.72 % SZS output start Proof
% See solution above
% 1.66/1.73 % Total time : 1.134000 s
% 1.66/1.73 % SZS output end Proof
% 1.66/1.73 % Total time : 1.137000 s
%------------------------------------------------------------------------------