TSTP Solution File: COL004-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL004-1 : 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 : n023.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 18:22:01 EDT 2023
% Result : Unsatisfiable 0.61s 1.01s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 18 unt; 5 typ; 0 def)
% Number of atoms : 18 ( 17 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 : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 7 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 ).
tff(decl_26,type,
g: $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_u_combinator,negated_conjecture,
apply(apply(X1,f(X1)),g(X1)) != apply(g(X1),apply(apply(f(X1),f(X1)),g(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_combinator) ).
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,plain,
apply(apply(apply(s,apply(s,k)),X1),X2) = apply(X1,X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,negated_conjecture,
apply(apply(X1,f(X1)),g(X1)) != apply(g(X1),apply(apply(f(X1),f(X1)),g(X1))),
prove_u_combinator ).
cnf(c_0_8,plain,
apply(apply(apply(s,apply(s,apply(s,k))),X1),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(X1,X3),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_11,negated_conjecture,
apply(apply(apply(s,apply(s,apply(s,k))),apply(f(X1),f(X1))),g(X1)) != apply(apply(X1,f(X1)),g(X1)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),X1)),X2) = apply(X2,X2),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_13,plain,
apply(apply(apply(s,apply(s,apply(k,X1))),X2),X3) = apply(X1,apply(X3,apply(X2,X3))),
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),X1)),f(X2))),g(X2)) != apply(apply(X2,f(X2)),g(X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
apply(X1,apply(apply(apply(s,apply(s,apply(s,k))),X2),X3)) = apply(apply(apply(s,apply(s,apply(k,X1))),X2),X3),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_16,negated_conjecture,
apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(s,apply(s,k)))))),apply(apply(s,k),X1)),f(X2)),g(X2)) != apply(apply(X2,f(X2)),g(X2)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n023.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 04:15:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.48/0.60 start to proof: theBenchmark
% 0.61/1.01 % Version : CSE_E---1.5
% 0.61/1.01 % Problem : theBenchmark.p
% 0.61/1.01 % Proof found
% 0.61/1.01 % SZS status Theorem for theBenchmark.p
% 0.61/1.01 % SZS output start Proof
% See solution above
% 0.61/1.01 % Total time : 0.394000 s
% 0.61/1.01 % SZS output end Proof
% 0.61/1.01 % Total time : 0.396000 s
%------------------------------------------------------------------------------