TSTP Solution File: GRP768-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP768-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 00:23:40 EDT 2023
% Result : Unsatisfiable 112.14s 112.29s
% Output : CNFRefutation 112.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 74 ( 63 unt; 11 typ; 0 def)
% Number of atoms : 63 ( 62 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 : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 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,
x0: $i ).
tff(decl_31,type,
x1: $i ).
tff(decl_32,type,
x2: $i ).
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(sos13,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(sos16,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(goals,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(sos19,axiom,
t(X1,X2) = quotient(product(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).
cnf(c_0_15,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_16,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_17,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_18,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_19,plain,
quotient(difference(X1,product(product(X1,X2),X3)),X3) = difference(product(X3,X1),product(X3,product(X1,X2))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_21,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_22,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_23,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
sos13 ).
cnf(c_0_24,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_26,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_27,plain,
quotient(difference(X1,product(X2,X3)),X3) = difference(product(X3,X1),product(X3,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
difference(X1,X1) = one,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
sos16 ).
cnf(c_0_30,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_31,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_23,c_0_18]),c_0_18]),c_0_24]) ).
cnf(c_0_32,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_18]),c_0_26]) ).
cnf(c_0_33,plain,
difference(product(X1,product(X2,X1)),product(X1,X2)) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
product(product(difference(X1,one),X1),product(X2,X3)) = product(product(product(difference(X1,one),X1),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_24]),c_0_24]) ).
cnf(c_0_35,plain,
difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_36,plain,
product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
product(product(X1,product(X2,X1)),quotient(one,X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_38,plain,
product(product(product(X1,quotient(one,X1)),X2),X3) = product(product(X1,quotient(one,X1)),product(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_32]),c_0_32]) ).
cnf(c_0_39,plain,
product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_20,c_0_35]) ).
cnf(c_0_40,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_41,plain,
product(product(X1,quotient(one,X1)),X1) = difference(difference(X1,one),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_22]) ).
cnf(c_0_42,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
goals ).
cnf(c_0_43,axiom,
t(X1,X2) = quotient(product(X1,X2),X1),
sos19 ).
cnf(c_0_44,plain,
product(product(X1,X2),quotient(one,X1)) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_45,plain,
product(product(X1,quotient(one,X1)),product(difference(product(X1,quotient(one,X1)),X2),X3)) = product(X2,X3),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_46,plain,
product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_47,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_48,plain,
difference(difference(product(X1,quotient(one,X1)),one),one) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_30]),c_0_22]) ).
cnf(c_0_49,plain,
difference(difference(X1,X2),product(product(difference(X1,X2),X3),X1)) = quotient(product(X3,X2),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_50,negated_conjecture,
quotient(product(product(difference(x0,one),x0),product(x1,x2)),product(difference(x0,one),x0)) != product(quotient(product(product(difference(x0,one),x0),x1),product(difference(x0,one),x0)),quotient(product(product(difference(x0,one),x0),x2),product(difference(x0,one),x0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_24]),c_0_24]),c_0_24]),c_0_43]),c_0_43]),c_0_43]) ).
cnf(c_0_51,plain,
product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_20]) ).
cnf(c_0_52,plain,
difference(product(X1,quotient(one,X1)),product(X2,X3)) = product(difference(product(X1,quotient(one,X1)),X2),X3),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_53,plain,
quotient(product(difference(X1,X2),X3),X1) = difference(X1,product(X2,quotient(X3,X1))),
inference(spm,[status(thm)],[c_0_21,c_0_46]) ).
cnf(c_0_54,plain,
quotient(one,product(X1,quotient(one,X1))) = difference(product(X1,quotient(one,X1)),one),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
product(X1,difference(product(X2,quotient(one,X2)),one)) = quotient(X1,product(X2,quotient(one,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_38]),c_0_21]),c_0_22]) ).
cnf(c_0_56,plain,
difference(X1,product(product(X1,product(X2,quotient(one,X2))),X3)) = product(product(X2,quotient(one,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_16]) ).
cnf(c_0_57,negated_conjecture,
product(quotient(product(product(x0,quotient(one,x0)),x1),product(x0,quotient(one,x0))),quotient(product(product(x0,quotient(one,x0)),x2),product(x0,quotient(one,x0)))) != quotient(product(product(x0,quotient(one,x0)),product(x1,x2)),product(x0,quotient(one,x0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_58,plain,
quotient(product(X1,X2),product(X3,quotient(one,X3))) = product(X1,quotient(X2,product(X3,quotient(one,X3)))),
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_51,c_0_52]),c_0_53]),c_0_52]),c_0_45]),c_0_54]),c_0_55]) ).
cnf(c_0_59,plain,
product(product(X1,product(X2,quotient(one,X2))),X3) = product(X1,product(product(X2,quotient(one,X2)),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
product(product(x0,quotient(one,x0)),product(quotient(x1,product(x0,quotient(one,x0))),product(product(x0,quotient(one,x0)),quotient(x2,product(x0,quotient(one,x0)))))) != product(product(x0,quotient(one,x0)),product(x1,quotient(x2,product(x0,quotient(one,x0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58]),c_0_38]),c_0_58]),c_0_58]) ).
cnf(c_0_61,plain,
product(quotient(X1,product(X2,quotient(one,X2))),product(product(X2,quotient(one,X2)),X3)) = product(X1,X3),
inference(spm,[status(thm)],[c_0_59,c_0_30]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : GRP768-1 : TPTP v8.1.2. Released v4.1.0.
% 0.05/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32 % Computer : n032.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Aug 29 00:31:46 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.57 start to proof: theBenchmark
% 112.14/112.29 % Version : CSE_E---1.5
% 112.14/112.29 % Problem : theBenchmark.p
% 112.14/112.29 % Proof found
% 112.14/112.29 % SZS status Theorem for theBenchmark.p
% 112.14/112.29 % SZS output start Proof
% See solution above
% 112.14/112.30 % Total time : 111.579000 s
% 112.14/112.30 % SZS output end Proof
% 112.14/112.30 % Total time : 111.586000 s
%------------------------------------------------------------------------------