TSTP Solution File: GRP048-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP048-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n004.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 00:13:50 EDT 2023
% Result : Unsatisfiable 12.39s 12.43s
% Output : CNFRefutation 12.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 61 ( 52 unt; 9 typ; 0 def)
% Number of atoms : 52 ( 51 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 : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 77 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
identity: $i ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
true: $i ).
tff(decl_26,type,
inverse: $i > $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
equalish: ( $i * $i ) > $i ).
tff(decl_29,type,
a: $i ).
tff(decl_30,type,
b: $i ).
cnf(product_substitution3,axiom,
ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(left_identity,axiom,
product(identity,X1,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(total_function2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
cnf(a_equals_b,hypothesis,
equalish(a,b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
cnf(associativity2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_inverse_substitution,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).
cnf(c_0_9,axiom,
ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
product_substitution3 ).
cnf(c_0_10,axiom,
product(identity,X1,X1) = true,
left_identity ).
cnf(c_0_11,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_12,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
total_function2 ).
cnf(c_0_13,plain,
ifeq(equalish(X1,X2),true,product(identity,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,hypothesis,
equalish(a,b) = true,
a_equals_b ).
cnf(c_0_15,plain,
ifeq(product(identity,X1,X2),true,equalish(X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).
cnf(c_0_16,hypothesis,
product(identity,a,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
cnf(c_0_17,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
associativity2 ).
cnf(c_0_18,hypothesis,
equalish(b,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]) ).
cnf(c_0_19,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(identity,X1,X4),true,product(X4,X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_11]) ).
cnf(c_0_20,hypothesis,
product(identity,b,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_11]) ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)) = true,
total_function1 ).
cnf(c_0_22,hypothesis,
ifeq(product(b,X1,X2),true,product(a,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]) ).
cnf(c_0_23,axiom,
product(inverse(X1),X1,identity) = true,
left_inverse ).
cnf(c_0_24,plain,
ifeq(product(X1,X2,X3),true,equalish(X3,multiply(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_11]) ).
cnf(c_0_25,hypothesis,
product(a,X1,multiply(b,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_11]) ).
cnf(c_0_26,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X1),X3,X4),true,product(identity,X2,X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_11]) ).
cnf(c_0_27,plain,
ifeq(equalish(multiply(X1,X2),X3),true,product(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_11]) ).
cnf(c_0_28,hypothesis,
equalish(multiply(b,X1),multiply(a,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11]) ).
cnf(c_0_29,plain,
ifeq(product(X1,X2,X3),true,product(identity,X2,multiply(inverse(X1),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_11]) ).
cnf(c_0_30,hypothesis,
product(b,X1,multiply(a,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_11]) ).
cnf(c_0_31,hypothesis,
product(identity,X1,multiply(inverse(b),multiply(a,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_11]) ).
cnf(c_0_32,hypothesis,
equalish(multiply(inverse(b),multiply(a,X1)),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_31]),c_0_11]) ).
cnf(c_0_33,plain,
ifeq(product(X1,X2,X1),true,product(identity,X2,identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_11]) ).
cnf(c_0_34,hypothesis,
product(inverse(b),multiply(a,X1),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_11]) ).
cnf(c_0_35,plain,
ifeq(product(identity,X1,X2),true,equalish(X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).
cnf(c_0_36,hypothesis,
product(identity,multiply(a,inverse(b)),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_11]) ).
cnf(c_0_37,hypothesis,
equalish(multiply(a,inverse(b)),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_11]) ).
cnf(c_0_38,hypothesis,
product(a,inverse(b),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_11]) ).
cnf(c_0_39,hypothesis,
product(identity,inverse(b),multiply(inverse(a),identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_11]) ).
cnf(c_0_40,hypothesis,
equalish(multiply(inverse(a),identity),inverse(b)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_39]),c_0_11]) ).
cnf(c_0_41,hypothesis,
product(inverse(a),identity,inverse(b)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_11]) ).
cnf(c_0_42,hypothesis,
product(identity,identity,multiply(inverse(inverse(a)),inverse(b))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_11]) ).
cnf(c_0_43,hypothesis,
equalish(multiply(inverse(inverse(a)),inverse(b)),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_42]),c_0_11]) ).
cnf(c_0_44,hypothesis,
product(inverse(inverse(a)),inverse(b),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_11]) ).
cnf(c_0_45,hypothesis,
product(identity,inverse(b),multiply(inverse(inverse(inverse(a))),identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_44]),c_0_11]) ).
cnf(c_0_46,hypothesis,
equalish(multiply(inverse(inverse(inverse(a))),identity),inverse(b)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_45]),c_0_11]) ).
cnf(c_0_47,plain,
ifeq(product(inverse(inverse(X1)),identity,X2),true,product(identity,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_11]) ).
cnf(c_0_48,hypothesis,
product(inverse(inverse(inverse(a))),identity,inverse(b)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_46]),c_0_11]) ).
cnf(c_0_49,hypothesis,
product(identity,inverse(a),inverse(b)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_11]) ).
cnf(c_0_50,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
prove_inverse_substitution ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_49]),c_0_11]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP048-10 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 20:09:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 12.39/12.43 % Version : CSE_E---1.5
% 12.39/12.43 % Problem : theBenchmark.p
% 12.39/12.43 % Proof found
% 12.39/12.43 % SZS status Theorem for theBenchmark.p
% 12.39/12.43 % SZS output start Proof
% See solution above
% 12.39/12.43 % Total time : 11.864000 s
% 12.39/12.43 % SZS output end Proof
% 12.39/12.43 % Total time : 11.867000 s
%------------------------------------------------------------------------------