TSTP Solution File: CAT004-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : CAT004-3 : 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 : n017.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 Aug 30 18:14:04 EDT 2023
% Result : Unsatisfiable 0.21s 0.75s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 28 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equivalent: ( $i * $i ) > $o ).
tff(decl_23,type,
there_exists: $i > $o ).
tff(decl_24,type,
domain: $i > $i ).
tff(decl_25,type,
codomain: $i > $i ).
tff(decl_26,type,
compose: ( $i * $i ) > $i ).
tff(decl_27,type,
f1: ( $i * $i ) > $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
h: $i ).
tff(decl_31,type,
g: $i ).
cnf(cancellation_for_product2,hypothesis,
( X1 = X3
| compose(X1,b) != X2
| compose(X3,b) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).
cnf(h_ab_equals_g_ab,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).
cnf(cancellation_for_product1,hypothesis,
( X1 = X3
| compose(X1,a) != X2
| compose(X3,a) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_5,hypothesis,
( X1 = X3
| compose(X1,b) != X2
| compose(X3,b) != X2 ),
cancellation_for_product2 ).
cnf(c_0_6,hypothesis,
( X1 = X2
| compose(X1,b) != compose(X2,b) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_7,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_8,hypothesis,
( compose(X1,X2) = X3
| compose(X1,compose(X2,b)) != compose(X3,b) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
h_ab_equals_g_ab ).
cnf(c_0_10,hypothesis,
( compose(g,a) = X1
| compose(h,compose(a,b)) != compose(X1,b) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,hypothesis,
( X1 = X3
| compose(X1,a) != X2
| compose(X3,a) != X2 ),
cancellation_for_product1 ).
cnf(c_0_12,hypothesis,
( compose(g,a) = compose(X1,X2)
| compose(h,compose(a,b)) != compose(X1,compose(X2,b)) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_13,hypothesis,
( X1 = X2
| compose(X1,a) != compose(X2,a) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
compose(g,a) = compose(h,a),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_15,hypothesis,
( g = X1
| compose(h,a) != compose(X1,a) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
h != g,
prove_h_equals_g ).
cnf(c_0_17,hypothesis,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CAT004-3 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 23:51:56 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.75 % Version : CSE_E---1.5
% 0.21/0.75 % Problem : theBenchmark.p
% 0.21/0.75 % Proof found
% 0.21/0.75 % SZS status Theorem for theBenchmark.p
% 0.21/0.75 % SZS output start Proof
% See solution above
% 0.21/0.75 % Total time : 0.177000 s
% 0.21/0.75 % SZS output end Proof
% 0.21/0.75 % Total time : 0.180000 s
%------------------------------------------------------------------------------