TSTP Solution File: COL066-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL066-1 : 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 : n014.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 18:22:26 EDT 2023
% Result : Unsatisfiable 69.18s 69.44s
% Output : CNFRefutation 69.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 25 ( 18 unt; 7 typ; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
b: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
q: $i ).
tff(decl_25,type,
w: $i ).
tff(decl_26,type,
f: $i > $i ).
tff(decl_27,type,
g: $i > $i ).
tff(decl_28,type,
h: $i > $i ).
cnf(prove_p_combinator,negated_conjecture,
apply(apply(apply(apply(X1,f(X1)),g(X1)),g(X1)),h(X1)) != apply(apply(f(X1),g(X1)),apply(apply(f(X1),g(X1)),h(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p_combinator) ).
cnf(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
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(q_definition,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).
cnf(c_0_4,negated_conjecture,
apply(apply(apply(apply(X1,f(X1)),g(X1)),g(X1)),h(X1)) != apply(apply(f(X1),g(X1)),apply(apply(f(X1),g(X1)),h(X1))),
prove_p_combinator ).
cnf(c_0_5,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_6,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_7,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
q_definition ).
cnf(c_0_8,negated_conjecture,
apply(apply(f(X1),g(X1)),apply(apply(f(X1),g(X1)),h(X1))) != apply(apply(apply(w,apply(X1,f(X1))),g(X1)),h(X1)),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_9,plain,
apply(apply(apply(w,b),X1),X2) = apply(X1,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_10,plain,
apply(apply(w,apply(apply(q,X1),X2)),X3) = apply(apply(X2,apply(X1,X3)),X3),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
apply(apply(apply(w,apply(X1,f(X1))),g(X1)),h(X1)) != apply(apply(apply(w,b),apply(f(X1),g(X1))),h(X1)),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
apply(apply(w,apply(apply(q,X1),apply(apply(q,X2),X3))),X4) = apply(apply(X3,apply(X2,apply(X1,X4))),X4),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_13,plain,
apply(apply(w,apply(q,X1)),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_14,negated_conjecture,
apply(apply(apply(w,apply(X1,apply(X2,f(apply(apply(b,X1),X2))))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))) != apply(apply(apply(w,b),apply(f(apply(apply(b,X1),X2)),g(apply(apply(b,X1),X2)))),h(apply(apply(b,X1),X2))),
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_15,plain,
apply(apply(w,apply(apply(w,apply(q,apply(q,X1))),apply(q,X2))),X3) = apply(apply(w,X1),apply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_7]),c_0_5]) ).
cnf(c_0_16,negated_conjecture,
apply(apply(apply(w,X1),apply(f(apply(apply(b,apply(w,apply(q,apply(q,X1)))),q)),g(apply(apply(b,apply(w,apply(q,apply(q,X1)))),q)))),h(apply(apply(b,apply(w,apply(q,apply(q,X1)))),q))) != apply(apply(apply(w,b),apply(f(apply(apply(b,apply(w,apply(q,apply(q,X1)))),q)),g(apply(apply(b,apply(w,apply(q,apply(q,X1)))),q)))),h(apply(apply(b,apply(w,apply(q,apply(q,X1)))),q))),
inference(spm,[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
% 0.00/0.12 % Problem : COL066-1 : 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
% 0.13/0.34 % Computer : n014.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 04:35:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 69.18/69.44 % Version : CSE_E---1.5
% 69.18/69.44 % Problem : theBenchmark.p
% 69.18/69.44 % Proof found
% 69.18/69.44 % SZS status Theorem for theBenchmark.p
% 69.18/69.44 % SZS output start Proof
% See solution above
% 69.18/69.44 % Total time : 68.719000 s
% 69.18/69.44 % SZS output end Proof
% 69.18/69.44 % Total time : 68.724000 s
%------------------------------------------------------------------------------