TSTP Solution File: COL034-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL034-1 : 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 : n015.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 18:22:09 EDT 2023
% Result : Unsatisfiable 2.72s 2.95s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 17 unt; 5 typ; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
b: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
m: $i ).
tff(decl_25,type,
t: $i ).
tff(decl_26,type,
f: $i > $i ).
cnf(prove_fixed_point,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(m_definition,axiom,
apply(m,X1) = apply(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
cnf(t_definition,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(c_0_4,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,axiom,
apply(m,X1) = apply(X1,X1),
m_definition ).
cnf(c_0_7,axiom,
apply(apply(t,X1),X2) = apply(X2,X1),
t_definition ).
cnf(c_0_8,negated_conjecture,
apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2))))) != apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_9,plain,
apply(X1,apply(X2,apply(apply(b,X1),X2))) = apply(m,apply(apply(b,X1),X2)),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_10,plain,
apply(m,apply(t,X1)) = apply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_11,negated_conjecture,
apply(f(apply(apply(b,X1),apply(apply(b,X2),X3))),apply(X1,apply(X2,apply(X3,f(apply(apply(b,X1),apply(apply(b,X2),X3))))))) != apply(X1,apply(X2,apply(X3,f(apply(apply(b,X1),apply(apply(b,X2),X3)))))),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_12,plain,
apply(X1,apply(X2,apply(X3,apply(apply(b,X1),apply(apply(b,X2),X3))))) = apply(m,apply(apply(b,X1),apply(apply(b,X2),X3))),
inference(spm,[status(thm)],[c_0_9,c_0_5]) ).
cnf(c_0_13,plain,
apply(m,apply(t,X1)) = apply(m,X1),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
apply(f(apply(apply(b,X1),apply(apply(b,apply(t,X2)),X3))),apply(X1,apply(apply(X3,f(apply(apply(b,X1),apply(apply(b,apply(t,X2)),X3)))),X2))) != apply(X1,apply(apply(X3,f(apply(apply(b,X1),apply(apply(b,apply(t,X2)),X3)))),X2)),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_15,plain,
apply(X1,apply(m,apply(apply(b,X1),apply(apply(b,m),t)))) = apply(m,apply(apply(b,X1),apply(apply(b,m),t))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL034-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n015.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 : Sun Aug 27 04:45:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 2.72/2.95 % Version : CSE_E---1.5
% 2.72/2.95 % Problem : theBenchmark.p
% 2.72/2.95 % Proof found
% 2.72/2.95 % SZS status Theorem for theBenchmark.p
% 2.72/2.95 % SZS output start Proof
% See solution above
% 2.72/2.95 % Total time : 2.369000 s
% 2.72/2.95 % SZS output end Proof
% 2.72/2.95 % Total time : 2.372000 s
%------------------------------------------------------------------------------