TSTP Solution File: GRP772-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP772-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : Thu Aug 31 00:23:41 EDT 2023
% Result : Unsatisfiable 0.70s 0.77s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 73 ( 61 unt; 12 typ; 0 def)
% Number of atoms : 61 ( 60 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 : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 142 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
one: $i ).
tff(decl_23,type,
product: ( $i * $i ) > $i ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
quotient: ( $i * $i ) > $i ).
tff(decl_26,type,
i: $i > $i ).
tff(decl_27,type,
j: $i > $i ).
tff(decl_28,type,
eta: $i > $i ).
tff(decl_29,type,
t: ( $i * $i ) > $i ).
tff(decl_30,type,
a: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c: ( $i * $i ) > $i ).
tff(decl_32,type,
x0: $i ).
tff(decl_33,type,
x1: $i ).
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(sos13,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos28,axiom,
product(product(X1,X2),a(X3,X4,X5)) = product(X1,product(X2,a(X3,X4,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos28) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos29,axiom,
product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos29) ).
cnf(sos27,axiom,
product(a(X1,X2,X3),product(X4,X5)) = product(product(a(X1,X2,X3),X4),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos27) ).
cnf(sos31,axiom,
a(i(X1),X2,X3) = a(j(X1),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos31) ).
cnf(sos32,axiom,
a(j(X1),X2,X3) = a(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos32) ).
cnf(sos30,axiom,
a(X1,i(X2),X3) = a(X1,j(X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos30) ).
cnf(goals,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_18,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_19,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_20,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
sos13 ).
cnf(c_0_21,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_23,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_24,plain,
product(difference(difference(X1,one),one),X2) = product(product(difference(X1,one),X1),product(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_19]),c_0_21]) ).
cnf(c_0_25,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
cnf(c_0_26,plain,
product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_28,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_29,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_30,axiom,
product(product(X1,X2),a(X3,X4,X5)) = product(X1,product(X2,a(X3,X4,X5))),
sos28 ).
cnf(c_0_31,plain,
product(product(X1,quotient(one,X1)),X1) = difference(difference(X1,one),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).
cnf(c_0_32,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_33,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_34,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
difference(difference(a(X1,X2,X3),one),one) = a(X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_27]) ).
cnf(c_0_36,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_37,axiom,
product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
sos29 ).
cnf(c_0_38,plain,
difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_39,plain,
quotient(one,a(X1,X2,X3)) = difference(a(X1,X2,X3),one),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,axiom,
product(a(X1,X2,X3),product(X4,X5)) = product(product(a(X1,X2,X3),X4),X5),
sos27 ).
cnf(c_0_41,axiom,
a(i(X1),X2,X3) = a(j(X1),X2,X3),
sos31 ).
cnf(c_0_42,axiom,
a(j(X1),X2,X3) = a(X2,X3,X1),
sos32 ).
cnf(c_0_43,plain,
difference(X1,product(a(X1,X2,X3),X1)) = difference(a(X2,X3,X1),one),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
product(X1,difference(a(X2,X3,X4),one)) = quotient(X1,a(X2,X3,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_36]),c_0_27]) ).
cnf(c_0_45,axiom,
a(X1,i(X2),X3) = a(X1,j(X2),X3),
sos30 ).
cnf(c_0_46,plain,
a(quotient(one,X1),X2,X3) = a(difference(X1,one),X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_19]),c_0_23]) ).
cnf(c_0_47,plain,
a(quotient(one,X1),X2,X3) = a(X2,X3,X1),
inference(rw,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_48,plain,
quotient(X1,a(X2,X3,X1)) = product(a(X1,X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_43]),c_0_44]) ).
cnf(c_0_49,plain,
a(X1,quotient(one,X2),X3) = a(X1,difference(X2,one),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_19]),c_0_23]) ).
cnf(c_0_50,plain,
a(difference(X1,one),X2,X3) = a(X2,X3,X1),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_52,plain,
product(a(X1,difference(X2,one),X3),X1) = quotient(X1,a(X3,X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_49]) ).
cnf(c_0_53,plain,
a(X1,X2,quotient(one,X3)) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
a(X1,X2,difference(X3,one)) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_34]) ).
cnf(c_0_55,plain,
quotient(X1,a(X1,X2,X3)) = product(a(X2,X3,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_47]) ).
cnf(c_0_56,plain,
difference(product(a(X1,X2,X3),X1),X1) = a(X2,X3,X1),
inference(spm,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_57,plain,
difference(product(a(X1,X2,X3),X3),X3) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_51,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
goals ).
cnf(c_0_59,plain,
a(X1,X1,X2) = a(X2,X1,X1),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP772-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 01:08:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.70/0.77 % Version : CSE_E---1.5
% 0.70/0.77 % Problem : theBenchmark.p
% 0.70/0.77 % Proof found
% 0.70/0.77 % SZS status Theorem for theBenchmark.p
% 0.70/0.77 % SZS output start Proof
% See solution above
% 0.70/0.77 % Total time : 0.185000 s
% 0.70/0.77 % SZS output end Proof
% 0.70/0.77 % Total time : 0.188000 s
%------------------------------------------------------------------------------