TSTP Solution File: GRP767-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP767-1 : 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 : n002.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 0.77s 0.90s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of formulae : 86 ( 75 unt; 11 typ; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 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,
l: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
t: ( $i * $i ) > $i ).
tff(decl_31,type,
x0: $i ).
tff(decl_32,type,
x1: $i ).
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(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
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(sos14,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos16,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
cnf(goals,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_15,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_16,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_17,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_18,plain,
difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_20,plain,
product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
quotient(product(X1,quotient(product(X2,X3),X1)),quotient(X3,X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_23,plain,
quotient(product(X1,quotient(X2,X1)),quotient(one,X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
quotient(product(X1,X2),quotient(one,X1)) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_25,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_26,plain,
product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_27,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_28,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_29,plain,
difference(X1,quotient(X2,quotient(one,X1))) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
sos14 ).
cnf(c_0_31,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_32,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_34,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_35,plain,
product(difference(X1,product(X2,quotient(one,X1))),X1) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_36,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_37,plain,
product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_32]) ).
cnf(c_0_38,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_28]),c_0_31]) ).
cnf(c_0_39,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_34,c_0_15]) ).
cnf(c_0_40,plain,
difference(X1,product(X2,quotient(one,X1))) = quotient(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_41,plain,
difference(one,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_42,plain,
product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
product(quotient(one,X1),product(X1,X2)) = quotient(quotient(X2,X1),quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25]),c_0_16]),c_0_41]) ).
cnf(c_0_44,plain,
quotient(product(quotient(one,quotient(one,X1)),X2),product(product(X1,quotient(one,X1)),X2)) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_42]) ).
cnf(c_0_45,plain,
quotient(quotient(quotient(X1,X2),quotient(one,X2)),product(X2,X1)) = quotient(one,X2),
inference(spm,[status(thm)],[c_0_19,c_0_43]) ).
cnf(c_0_46,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
sos16 ).
cnf(c_0_47,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_48,plain,
quotient(one,product(product(X1,quotient(one,X1)),quotient(one,X1))) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_16]) ).
cnf(c_0_49,plain,
quotient(quotient(X1,quotient(one,X2)),product(X2,product(X1,X2))) = quotient(one,X2),
inference(spm,[status(thm)],[c_0_45,c_0_19]) ).
cnf(c_0_50,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_46,c_0_32]),c_0_32]) ).
cnf(c_0_51,plain,
product(product(X1,quotient(one,X1)),quotient(one,X1)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
product(quotient(one,X1),quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_53,plain,
product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_40]) ).
cnf(c_0_54,plain,
difference(quotient(one,X1),quotient(X2,quotient(one,X1))) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_55,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_50,c_0_38]),c_0_38]) ).
cnf(c_0_56,plain,
product(product(X1,quotient(one,X1)),quotient(one,quotient(one,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_47]) ).
cnf(c_0_57,plain,
product(X1,product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_22]),c_0_22]) ).
cnf(c_0_58,plain,
product(quotient(X1,quotient(one,X2)),quotient(one,quotient(one,X2))) = quotient(product(X1,X2),quotient(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_24]),c_0_43]),c_0_19]) ).
cnf(c_0_59,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_60,plain,
quotient(product(X1,quotient(X2,X1)),quotient(X3,X1)) = product(X1,quotient(X2,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_61,plain,
quotient(product(X1,quotient(one,X1)),X1) = difference(X1,one),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_62,plain,
quotient(one,quotient(one,product(X1,quotient(one,X1)))) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52]),c_0_57]) ).
cnf(c_0_63,plain,
product(quotient(X1,X2),quotient(one,X2)) = quotient(product(X1,difference(X2,one)),X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
product(X1,quotient(product(X1,quotient(one,X1)),X2)) = quotient(one,quotient(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_17]) ).
cnf(c_0_65,plain,
quotient(one,product(X1,quotient(one,X1))) = difference(product(X1,quotient(one,X1)),one),
inference(spm,[status(thm)],[c_0_47,c_0_62]) ).
cnf(c_0_66,plain,
quotient(product(product(X1,X2),difference(X2,one)),X2) = product(X1,quotient(one,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_19]) ).
cnf(c_0_67,plain,
quotient(product(X1,quotient(one,X1)),X2) = difference(X1,quotient(one,quotient(X2,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_64]) ).
cnf(c_0_68,plain,
product(product(X1,quotient(one,X1)),quotient(one,X2)) = quotient(one,quotient(X2,product(X1,quotient(one,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_65]),c_0_17]) ).
cnf(c_0_69,plain,
quotient(one,quotient(X1,product(X2,quotient(one,X2)))) = difference(X2,quotient(one,quotient(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_55]),c_0_17]),c_0_22]),c_0_67]),c_0_68]) ).
cnf(c_0_70,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
goals ).
cnf(c_0_71,plain,
product(product(X1,quotient(one,X1)),quotient(one,X2)) = difference(X1,quotient(one,quotient(X2,X1))),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
product(quotient(one,quotient(one,x0)),quotient(one,product(x1,x0))) != quotient(one,x1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_73,plain,
product(quotient(one,quotient(one,X1)),quotient(one,X2)) = quotient(one,quotient(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_71]),c_0_17]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP767-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 : Mon Aug 28 23:12:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.77/0.90 % Version : CSE_E---1.5
% 0.77/0.90 % Problem : theBenchmark.p
% 0.77/0.90 % Proof found
% 0.77/0.90 % SZS status Theorem for theBenchmark.p
% 0.77/0.90 % SZS output start Proof
% See solution above
% 0.77/0.90 % Total time : 0.328000 s
% 0.77/0.90 % SZS output end Proof
% 0.77/0.90 % Total time : 0.331000 s
%------------------------------------------------------------------------------