%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : TOP021+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.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 : Wed Apr 9 10:52:24 PM UTC 2025
% Result : Theorem 2.49s 1.62s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 6 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ an_open_function_from_onto > a_continuous_function_from_onto > a_locally_compact_top_space > the_projection_function > the_product_top_space_over > apply > #nlpp > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(the_projection_function,type,
the_projection_function: ( $i * $i * $i ) > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(a_continuous_function_from_onto,type,
a_continuous_function_from_onto: ( $i * $i * $i ) > $o ).
tff(the_product_top_space_over,type,
the_product_top_space_over: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(a_locally_compact_top_space,type,
a_locally_compact_top_space: $i > $o ).
tff(an_open_function_from_onto,type,
an_open_function_from_onto: ( $i * $i * $i ) > $o ).
tff(f_47,negated_conjecture,
~ ! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_5_19a) ).
tff(f_28,axiom,
! [A,X,A1] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p90a) ).
tff(f_31,axiom,
! [A,X,A1,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_3_2) ).
tff(f_40,axiom,
! [F,A,B] :
( ( an_open_function_from_onto(F,A,B)
& a_continuous_function_from_onto(F,A,B)
& a_locally_compact_top_space(A) )
=> a_locally_compact_top_space(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p_147e) ).
tff(c_10,plain,
a_locally_compact_top_space(the_product_top_space_over('#skF_1','#skF_2')),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_2,plain,
! [A_1,X_2,A1_3] : a_continuous_function_from_onto(the_projection_function(A_1,X_2,A1_3),the_product_top_space_over(X_2,A1_3),apply(X_2,A_1)),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_4,plain,
! [A_4,X_5,A1_6,X1_7] : an_open_function_from_onto(the_projection_function(A_4,X_5,A1_6),the_product_top_space_over(X1_7,A1_6),apply(X1_7,A_4)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_13,plain,
! [B_19,A_20,F_21] :
( a_locally_compact_top_space(B_19)
| ~ a_locally_compact_top_space(A_20)
| ~ a_continuous_function_from_onto(F_21,A_20,B_19)
| ~ an_open_function_from_onto(F_21,A_20,B_19) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_18,plain,
! [X1_22,A_23,A1_24,X_25] :
( a_locally_compact_top_space(apply(X1_22,A_23))
| ~ a_locally_compact_top_space(the_product_top_space_over(X1_22,A1_24))
| ~ a_continuous_function_from_onto(the_projection_function(A_23,X_25,A1_24),the_product_top_space_over(X1_22,A1_24),apply(X1_22,A_23)) ),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_23,plain,
! [X_26,A_27,A1_28] :
( a_locally_compact_top_space(apply(X_26,A_27))
| ~ a_locally_compact_top_space(the_product_top_space_over(X_26,A1_28)) ),
inference(resolution,[status(thm)],[c_2,c_18]) ).
tff(c_26,plain,
! [A_27] : a_locally_compact_top_space(apply('#skF_1',A_27)),
inference(resolution,[status(thm)],[c_10,c_23]) ).
tff(c_8,plain,
~ a_locally_compact_top_space(apply('#skF_1','#skF_3')),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_29,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : TOP021+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Apr 9 10:31:22 EDT 2025
% 0.15/0.36 % CPUTime :
% 2.49/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.71/1.63
% 2.71/1.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------