TSTP Solution File: GRP124-6.004 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 00:16:13 EDT 2023
% Result : Unsatisfiable 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 85 ( 28 unt; 8 typ; 0 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 60 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 57 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
e_1: $i ).
tff(decl_23,type,
group_element: $i > $o ).
tff(decl_24,type,
e_2: $i ).
tff(decl_25,type,
e_3: $i ).
tff(decl_26,type,
e_4: $i ).
tff(decl_27,type,
equalish: ( $i * $i ) > $o ).
tff(decl_28,type,
product1: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
product2: ( $i * $i * $i ) > $o ).
cnf(product1_total_function1,axiom,
( product1(X1,X2,e_1)
| product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| product1(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(product1_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
cnf(product1_idempotence,axiom,
product1(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(product1_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(product2_total_function2,axiom,
( equalish(X3,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
cnf(product2_idempotence,axiom,
product2(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
cnf(qg2a,negated_conjecture,
( product2(X4,X2,X1)
| ~ product1(X1,X2,X3)
| ~ product1(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2a) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(c_0_16,axiom,
( product1(X1,X2,e_1)
| product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| product1(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
product1_total_function1 ).
cnf(c_0_17,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_18,axiom,
( equalish(X2,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X4,X3) ),
product1_right_cancellation ).
cnf(c_0_19,axiom,
product1(X1,X1,X1),
product1_idempotence ).
cnf(c_0_20,plain,
( product1(X1,e_4,e_4)
| product1(X1,e_4,e_3)
| product1(X1,e_4,e_2)
| product1(X1,e_4,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_22,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_23,axiom,
( equalish(X1,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X4,X2,X3) ),
product1_left_cancellation ).
cnf(c_0_24,plain,
( equalish(X1,X2)
| ~ product1(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1 ).
cnf(c_0_27,plain,
( product1(X1,e_3,e_4)
| product1(X1,e_3,e_3)
| product1(X1,e_3,e_2)
| product1(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_28,plain,
( equalish(X1,X2)
| ~ product1(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_29,plain,
( product1(e_1,e_4,e_4)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4 ).
cnf(c_0_31,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_32,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_33,plain,
( product1(X1,e_1,e_4)
| product1(X1,e_1,e_3)
| product1(X1,e_1,e_2)
| product1(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_34,axiom,
( equalish(X3,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X2,X4) ),
product2_total_function2 ).
cnf(c_0_35,axiom,
product2(X1,X1,X1),
product2_idempotence ).
cnf(c_0_36,negated_conjecture,
( product2(X4,X2,X1)
| ~ product1(X1,X2,X3)
| ~ product1(X3,X1,X4) ),
qg2a ).
cnf(c_0_37,plain,
( product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_38,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_32]) ).
cnf(c_0_39,plain,
( product1(e_4,e_1,e_1)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_3)
| product1(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_40,plain,
( equalish(X1,X2)
| ~ product2(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( product2(e_3,X1,e_4)
| product1(e_1,e_4,e_2)
| ~ product1(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_43,negated_conjecture,
( product2(e_4,X1,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3)
| ~ product1(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_44,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_45,plain,
( product1(e_4,e_1,e_4)
| product1(e_4,e_1,e_3)
| product1(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_26]) ).
cnf(c_0_46,negated_conjecture,
( product1(e_1,e_4,e_2)
| ~ product1(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| ~ product1(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_44]) ).
cnf(c_0_48,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_49,plain,
( product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_45]),c_0_30]) ).
cnf(c_0_50,negated_conjecture,
( equalish(X1,e_4)
| ~ product1(e_4,e_3,e_1)
| ~ product1(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( product1(e_1,e_3,e_2)
| ~ product1(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( product2(e_3,X1,e_1)
| product1(e_4,e_1,e_2)
| ~ product1(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( ~ product1(e_4,e_3,e_1)
| ~ product1(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_44]) ).
cnf(c_0_54,plain,
( product1(e_4,e_3,e_1)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_55,negated_conjecture,
( product1(e_4,e_1,e_2)
| ~ product1(e_1,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_52]),c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| ~ product1(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3)
| product1(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_55,c_0_38]) ).
cnf(c_0_58,negated_conjecture,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3)
| ~ product1(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_56]),c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( product1(e_4,e_1,e_2)
| product1(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_57]),c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( product1(e_4,e_3,e_2)
| ~ product1(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_42]) ).
cnf(c_0_61,negated_conjecture,
( product1(e_4,e_1,e_2)
| equalish(X1,e_1)
| ~ product1(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( equalish(X1,e_3)
| ~ product1(e_3,e_4,e_1)
| ~ product1(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( product1(e_4,e_1,e_2)
| ~ product1(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_60]),c_0_26]) ).
cnf(c_0_64,plain,
( product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_65,negated_conjecture,
~ product1(e_3,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_48]) ).
cnf(c_0_66,plain,
( product1(e_3,e_4,e_4)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_66]),c_0_44]) ).
cnf(c_0_68,plain,
product1(e_3,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_67]),c_0_42]) ).
cnf(c_0_69,plain,
( equalish(X1,e_3)
| ~ product1(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_68]) ).
cnf(c_0_70,negated_conjecture,
~ product1(e_4,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_46]),c_0_48]) ).
cnf(c_0_71,plain,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_54,c_0_70]) ).
cnf(c_0_72,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_71]),c_0_44]) ).
cnf(c_0_73,plain,
product1(e_4,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_72]),c_0_42]) ).
cnf(c_0_74,plain,
( equalish(X1,e_3)
| ~ product1(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_73]) ).
cnf(c_0_75,negated_conjecture,
product1(e_4,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_73]),c_0_26]) ).
cnf(c_0_76,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n012.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 21:30:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.029000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.032000 s
%------------------------------------------------------------------------------