TSTP Solution File: GRP128-4.003 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 00:16:56 EDT 2023
% Result : Unsatisfiable 0.57s 0.64s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 66 ( 20 unt; 6 typ; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 176 ( 81 ~; 95 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 67 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
group_element: $i > $o ).
tff(decl_23,type,
e_1: $i ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
e_2: $i ).
tff(decl_26,type,
e_3: $i ).
tff(decl_27,type,
equalish: ( $i * $i ) > $o ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(column_surjectivity,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(qg3,negated_conjecture,
( product(X1,X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(qg3_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X3)
| ~ product(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_2) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_0_15,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_16,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_17,plain,
( equalish(X1,X2)
| product(X3,X2,e_3)
| product(X3,X2,e_2)
| ~ product(X3,X1,e_1)
| ~ group_element(X2)
| ~ group_element(X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
column_surjectivity ).
cnf(c_0_19,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_20,plain,
( equalish(e_1,X1)
| product(X2,e_3,e_1)
| product(X2,e_2,e_1)
| product(X2,X1,e_2)
| product(X2,X1,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_21,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_22,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_23,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_24,plain,
( product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_2,e_1)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_26,plain,
( equalish(X1,X2)
| product(X2,e_2,e_1)
| product(X2,e_3,e_2)
| product(X2,e_3,e_3)
| ~ product(X1,e_3,e_1)
| ~ group_element(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( product(X1,X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X3,X2,X4) ),
qg3 ).
cnf(c_0_28,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19])]),c_0_27]) ).
cnf(c_0_29,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_30,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X3)
| ~ product(X4,X2,X1) ),
qg3_2 ).
cnf(c_0_31,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_32,plain,
( equalish(X1,e_1)
| product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_33,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_21])]),c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( product(e_1,e_2,e_1)
| product(e_3,e_3,X1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_35,plain,
( product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( equalish(X1,e_3)
| product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_35]) ).
cnf(c_0_38,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_39,plain,
( product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( equalish(X1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_41,plain,
( equalish(X1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_3)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_43,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_44,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( product(e_3,e_2,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_16]),c_0_43]),c_0_21])]),c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( product(e_2,e_2,X1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_47]),c_0_48]) ).
cnf(c_0_50,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_16]),c_0_21]),c_0_43])]) ).
cnf(c_0_51,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_52,negated_conjecture,
( equalish(X1,e_2)
| product(e_2,e_3,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( product(e_2,e_3,e_2)
| ~ product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_3,X1)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
product(e_2,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_15,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( product(X1,e_2,e_2)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
~ product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n009.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 : Tue Aug 29 02:20:05 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.55/0.59 start to proof: theBenchmark
% 0.57/0.64 % Version : CSE_E---1.5
% 0.57/0.64 % Problem : theBenchmark.p
% 0.57/0.64 % Proof found
% 0.57/0.64 % SZS status Theorem for theBenchmark.p
% 0.57/0.64 % SZS output start Proof
% See solution above
% 0.57/0.64 % Total time : 0.043000 s
% 0.57/0.64 % SZS output end Proof
% 0.57/0.64 % Total time : 0.046000 s
%------------------------------------------------------------------------------