TSTP Solution File: COL006-7 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL006-7 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 18:22:03 EDT 2023
% Result : Unsatisfiable 205.83s 205.85s
% Output : CNFRefutation 205.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 48 unt; 5 typ; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 13 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,
strong_fixed_point: $i ).
tff(decl_26,type,
fixed_pt: $i ).
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(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
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,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_6,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,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_6]) ).
cnf(c_0_8,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_9,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_10,plain,
apply(apply(apply(s,apply(s,apply(k,apply(k,X1)))),X2),X3) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_11,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
strong_fixed_point ).
cnf(c_0_12,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_8]) ).
cnf(c_0_13,plain,
apply(apply(apply(s,X1),apply(k,X2)),X3) = apply(apply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_14,plain,
apply(apply(apply(s,apply(apply(s,s),X1)),X2),apply(s,apply(k,apply(k,X3)))) = X3,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_11]),c_0_5]),c_0_6]),c_0_12]) ).
cnf(c_0_16,plain,
apply(apply(apply(s,apply(s,X1)),X2),apply(k,X3)) = apply(apply(X1,apply(X2,apply(k,X3))),X3),
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_17,plain,
apply(strong_fixed_point,apply(k,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
apply(apply(apply(s,apply(s,X1)),apply(apply(s,k),X2)),X3) = apply(apply(X1,X3),apply(X3,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
cnf(c_0_19,plain,
apply(apply(apply(s,apply(s,X1)),strong_fixed_point),apply(k,X2)) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,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_21,plain,
apply(apply(apply(s,apply(s,k)),X1),X2) = apply(X1,X2),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_22,plain,
apply(apply(apply(s,strong_fixed_point),X1),apply(k,X2)) = apply(X2,apply(X1,apply(k,X2))),
inference(spm,[status(thm)],[c_0_4,c_0_17]) ).
cnf(c_0_23,plain,
apply(apply(apply(apply(s,X1),X2),X3),apply(X4,apply(X2,X3))) = apply(apply(apply(s,apply(X1,X3)),X4),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_24,plain,
apply(apply(apply(s,apply(s,strong_fixed_point)),apply(apply(s,k),X1)),apply(k,X2)) = apply(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_5]) ).
cnf(c_0_25,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,apply(s,X1)),strong_fixed_point),apply(k,X3)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_26,plain,
apply(apply(apply(apply(s,s),apply(apply(s,k),X1)),X2),X3) = apply(apply(X2,X3),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
cnf(c_0_27,plain,
apply(apply(apply(apply(s,s),apply(s,apply(s,k))),X1),X2) = apply(apply(X1,X2),apply(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X1)) = apply(X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_29,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X1),X2) = apply(apply(X1,X2),X2),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_30,plain,
apply(apply(apply(apply(s,X1),apply(apply(s,X2),X3)),X4),apply(X5,apply(apply(X2,X4),apply(X3,X4)))) = apply(apply(apply(s,apply(X1,X4)),X5),apply(apply(X2,X4),apply(X3,X4))),
inference(spm,[status(thm)],[c_0_23,c_0_4]) ).
cnf(c_0_31,plain,
apply(apply(apply(s,apply(s,apply(s,strong_fixed_point))),strong_fixed_point),apply(k,apply(k,X1))) = apply(X1,X1),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
apply(apply(apply(apply(s,s),apply(apply(s,k),X1)),X2),X3) = apply(apply(apply(apply(s,s),apply(s,apply(s,k))),X2),X3),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
apply(apply(apply(apply(s,s),apply(s,apply(s,k))),X1),X2) = apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,apply(X1,X2))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1))),X2) = apply(X1,apply(X2,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_29]) ).
cnf(c_0_35,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X1),X2) = apply(apply(apply(s,apply(s,X1)),strong_fixed_point),apply(k,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_36,plain,
apply(apply(X1,apply(apply(apply(s,X2),X3),X4)),apply(X5,apply(apply(X2,X4),apply(X3,X4)))) = apply(apply(apply(s,X1),X5),apply(apply(X2,X4),apply(X3,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_6]),c_0_5]) ).
cnf(c_0_37,plain,
apply(apply(apply(s,apply(s,apply(s,strong_fixed_point))),strong_fixed_point),apply(k,apply(k,X1))) = apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_38,plain,
apply(apply(apply(apply(s,apply(s,s)),strong_fixed_point),apply(k,apply(apply(s,s),apply(s,k)))),apply(s,apply(k,X1))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_39,plain,
apply(apply(apply(apply(s,apply(s,s)),strong_fixed_point),apply(k,X1)),X2) = apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,apply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_25]),c_0_33]) ).
cnf(c_0_40,plain,
apply(apply(apply(s,apply(s,apply(s,apply(k,X1)))),strong_fixed_point),apply(k,X2)) = apply(X1,apply(X2,X2)),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
apply(apply(X1,apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X2))),apply(X3,apply(X2,X2))) = apply(apply(apply(s,X1),X3),apply(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_17]),c_0_13]),c_0_13]),c_0_17]),c_0_17]),c_0_13]),c_0_13]),c_0_17]) ).
cnf(c_0_42,plain,
apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1))))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
apply(apply(apply(s,apply(s,apply(s,apply(k,X1)))),strong_fixed_point),apply(k,X2)) = apply(X1,apply(apply(apply(s,strong_fixed_point),strong_fixed_point),apply(k,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_44,plain,
apply(apply(X1,apply(strong_fixed_point,X2)),apply(X3,apply(X2,apply(strong_fixed_point,X2)))) = apply(apply(apply(s,X1),X3),apply(X2,apply(strong_fixed_point,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_35]),c_0_43]),c_0_42]),c_0_35]),c_0_43]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
prove_strong_fixed_point ).
cnf(c_0_46,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_44]),c_0_8]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL006-7 : TPTP v8.1.2. Released v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sun Aug 27 05:01:24 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 205.83/205.85 % Version : CSE_E---1.5
% 205.83/205.85 % Problem : theBenchmark.p
% 205.83/205.85 % Proof found
% 205.83/205.85 % SZS status Theorem for theBenchmark.p
% 205.83/205.85 % SZS output start Proof
% See solution above
% 205.83/205.86 % Total time : 205.224000 s
% 205.83/205.86 % SZS output end Proof
% 205.83/205.86 % Total time : 205.236000 s
%------------------------------------------------------------------------------