TSTP Solution File: HAL003+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 43
% Syntax : Number of formulae : 58 ( 6 unt; 38 typ; 0 def)
% Number of atoms : 57 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 63 ( 26 ~; 25 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 24 >; 34 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 14 con; 0-6 aty)
% Number of variables : 38 ( 0 sgn; 16 !; 3 ?; 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_1: $i > $i ).
tff(decl_59,type,
esk15_1: $i > $i ).
fof(properties_for_surjection,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X7] :
( element(X7,X3)
=> ? [X8] :
( element(X8,X2)
& apply(X1,X8) = X7 ) ) )
=> surjection(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_surjection) ).
fof(subtract_in_domain,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> element(subtract(X2,X5,X6),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(lemma12,axiom,
! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).
fof(g_surjection,conjecture,
surjection(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_surjection) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(c_0_5,plain,
! [X44,X45,X46,X48] :
( ( element(esk4_3(X44,X45,X46),X46)
| ~ morphism(X44,X45,X46)
| surjection(X44) )
& ( ~ element(X48,X45)
| apply(X44,X48) != esk4_3(X44,X45,X46)
| ~ morphism(X44,X45,X46)
| surjection(X44) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[properties_for_surjection])])])])])]) ).
fof(c_0_6,plain,
! [X84,X85,X86] :
( ~ element(X85,X84)
| ~ element(X86,X84)
| element(subtract(X84,X85,X86),X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).
cnf(c_0_7,plain,
( surjection(X3)
| ~ element(X1,X2)
| apply(X3,X1) != esk4_3(X3,X2,X4)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( element(subtract(X2,X1,X3),X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X104] :
( ( element(esk14_1(X104),b)
| ~ element(X104,e) )
& ( element(esk15_1(X104),b)
| ~ element(X104,e) )
& ( apply(g,subtract(b,esk14_1(X104),esk15_1(X104))) = X104
| ~ element(X104,e) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma12])])])]) ).
fof(c_0_10,negated_conjecture,
~ surjection(g),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[g_surjection])]) ).
cnf(c_0_11,plain,
( surjection(X1)
| apply(X1,subtract(X2,X3,X4)) != esk4_3(X1,X2,X5)
| ~ element(X4,X2)
| ~ element(X3,X2)
| ~ morphism(X1,X2,X5) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( apply(g,subtract(b,esk14_1(X1),esk15_1(X1))) = X1
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
~ surjection(g),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( element(esk14_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( element(esk15_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ element(esk4_3(g,b,X1),e)
| ~ morphism(g,b,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
( element(esk4_3(X1,X2,X3),X3)
| surjection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_19,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.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 : Mon Aug 28 02:51:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 0.20/0.57 % Version : CSE_E---1.5
% 0.20/0.57 % Problem : theBenchmark.p
% 0.20/0.57 % Proof found
% 0.20/0.57 % SZS status Theorem for theBenchmark.p
% 0.20/0.57 % SZS output start Proof
% See solution above
% 0.20/0.57 % Total time : 0.023000 s
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57 % Total time : 0.026000 s
%------------------------------------------------------------------------------