TSTP Solution File: COL002-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL002-2 : 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 : n026.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 18:21:56 EDT 2023
% Result : Unsatisfiable 1.03s 1.11s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 33 ( 20 unt; 7 typ; 0 def)
% Number of atoms : 32 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
s: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
b: $i ).
tff(decl_25,type,
c: $i ).
tff(decl_26,type,
i: $i ).
tff(decl_27,type,
fixed_pt: $i ).
tff(decl_28,type,
fixed_point: $i > $o ).
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(c_definition,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
cnf(i_definition,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
cnf(weak_fixed_point,axiom,
( fixed_point(X1)
| X1 != apply(fixed_pt,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
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_weak_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
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(c,X1),X2),X3) = apply(apply(X1,X3),X2),
c_definition ).
cnf(c_0_8,axiom,
apply(i,X1) = X1,
i_definition ).
cnf(c_0_9,axiom,
( fixed_point(X1)
| X1 != apply(fixed_pt,X1) ),
weak_fixed_point ).
cnf(c_0_10,plain,
apply(apply(apply(c,apply(b,X1)),X2),X3) = apply(X1,apply(X3,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
apply(apply(apply(c,i),X1),X2) = apply(X2,X1),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_13,plain,
( fixed_point(apply(X1,X2))
| apply(apply(apply(c,apply(b,fixed_pt)),X2),X1) != apply(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
apply(apply(apply(c,i),X1),apply(apply(c,X2),X3)) = apply(apply(X2,X1),X3),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_15,plain,
apply(apply(apply(c,apply(b,X1)),X2),apply(apply(c,i),X3)) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
apply(apply(apply(s,X1),i),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_17,plain,
( fixed_point(apply(apply(X1,X2),X3))
| apply(fixed_pt,apply(apply(apply(c,X1),X3),X2)) != apply(apply(X1,X2),X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
apply(apply(apply(c,apply(s,X1)),X2),i) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_19,plain,
apply(apply(apply(c,apply(c,X1)),X2),X3) = apply(apply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_20,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),
prove_weak_fixed_point ).
cnf(c_0_21,plain,
( fixed_point(apply(apply(X1,X2),X2))
| apply(fixed_pt,apply(apply(apply(s,X1),i),X2)) != apply(apply(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ fixed_point(apply(apply(apply(c,i),i),apply(apply(c,apply(s,apply(b,X1))),apply(apply(s,apply(b,X1)),i)))),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_23,plain,
( fixed_point(apply(X1,apply(X2,X2)))
| apply(fixed_pt,apply(apply(apply(s,apply(b,X1)),i),X2)) != apply(X1,apply(X2,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_6]) ).
cnf(c_0_24,negated_conjecture,
~ fixed_point(apply(X1,apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_7]),c_0_8]),c_0_18]),c_0_6]) ).
cnf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL002-2 : 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 : n026.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 04:27:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 1.03/1.11 % Version : CSE_E---1.5
% 1.03/1.11 % Problem : theBenchmark.p
% 1.03/1.11 % Proof found
% 1.03/1.11 % SZS status Theorem for theBenchmark.p
% 1.03/1.11 % SZS output start Proof
% See solution above
% 1.03/1.11 % Total time : 0.535000 s
% 1.03/1.11 % SZS output end Proof
% 1.03/1.11 % Total time : 0.538000 s
%------------------------------------------------------------------------------