TSTP Solution File: COL006-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL006-1 : 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 : n005.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 18:22:02 EDT 2023
% Result : Unsatisfiable 194.48s 194.45s
% Output : CNFRefutation 194.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 16 unt; 4 typ; 0 def)
% Number of atoms : 16 ( 15 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 : 8 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
s: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
k: $i ).
tff(decl_25,type,
f: $i > $i ).
cnf(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
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(c_0_3,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_4,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_5,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_7,plain,
apply(apply(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(X3,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
apply(apply(apply(s,apply(apply(s,X1),X2)),X3),X4) = apply(apply(apply(X1,X4),apply(X2,X4)),apply(X3,X4)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_9,negated_conjecture,
apply(apply(apply(s,apply(apply(s,k),X1)),X2),f(X2)) != apply(X2,f(X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(apply(s,apply(k,X1)),X2)),X3),X4) = apply(apply(X1,apply(X2,X4)),apply(X3,X4)),
inference(spm,[status(thm)],[c_0_8,c_0_3]) ).
cnf(c_0_11,plain,
apply(apply(apply(apply(s,s),X1),X2),X3) = apply(apply(X2,X3),apply(apply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_12,negated_conjecture,
apply(apply(apply(apply(s,apply(apply(s,apply(k,s)),apply(s,k))),X1),X2),f(apply(X1,X2))) != apply(apply(X1,X2),f(apply(X1,X2))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X1),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
cnf(c_0_14,negated_conjecture,
apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(apply(s,apply(k,s)),apply(s,k)))),X1),f(apply(X1,X1))) != apply(apply(X1,X1),f(apply(X1,X1))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.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 : Sun Aug 27 04:55:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 194.48/194.45 % Version : CSE_E---1.5
% 194.48/194.45 % Problem : theBenchmark.p
% 194.48/194.45 % Proof found
% 194.48/194.45 % SZS status Theorem for theBenchmark.p
% 194.48/194.45 % SZS output start Proof
% See solution above
% 194.48/194.45 % Total time : 193.889000 s
% 194.48/194.45 % SZS output end Proof
% 194.48/194.45 % Total time : 193.899000 s
%------------------------------------------------------------------------------