TSTP Solution File: GRP123-7.003 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP123-7.003 : 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 : n024.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 00:16:11 EDT 2023
% Result : Unsatisfiable 0.18s 0.57s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 65 ( 28 unt; 10 typ; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 99 ( 48 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 7 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 54 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
e_1: $i ).
tff(decl_23,type,
e_2: $i ).
tff(decl_24,type,
next: ( $i * $i ) > $o ).
tff(decl_25,type,
e_3: $i ).
tff(decl_26,type,
greater: ( $i * $i ) > $o ).
tff(decl_27,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
group_element: $i > $o ).
tff(decl_29,type,
equalish: ( $i * $i ) > $o ).
tff(decl_30,type,
product1: ( $i * $i * $i ) > $o ).
tff(decl_31,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)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
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(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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
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(product1_idempotence,axiom,
product1(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
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(qg1a,negated_conjecture,
( product2(X4,X1,X2)
| ~ product1(X1,X2,X3)
| ~ product1(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
cnf(c_0_13,axiom,
( product1(X1,X2,e_1)
| product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product1_total_function1 ).
cnf(c_0_14,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_15,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_16,axiom,
( equalish(X2,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X4,X3) ),
product1_right_cancellation ).
cnf(c_0_17,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_18,axiom,
( equalish(X1,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X4,X2,X3) ),
product1_left_cancellation ).
cnf(c_0_19,plain,
( 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_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ product1(X1,e_1,X2)
| ~ product1(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
product1(X1,X1,X1),
product1_idempotence ).
cnf(c_0_22,plain,
( 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_13,c_0_17]) ).
cnf(c_0_23,plain,
( ~ product1(e_1,X1,X2)
| ~ product1(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_24,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_25,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_26,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_27,plain,
~ product1(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_29,plain,
( product1(e_3,e_1,e_1)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_30,plain,
~ product1(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_31,axiom,
( equalish(X3,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X2,X4) ),
product2_total_function2 ).
cnf(c_0_32,plain,
( product1(X1,e_2,e_3)
| product1(X1,e_2,e_2)
| product1(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_33,plain,
( ~ product1(X1,e_1,X2)
| ~ product1(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_34,plain,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( ~ product1(X1,e_2,X2)
| ~ product1(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_36,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( ~ product2(X1,X2,e_2)
| ~ product2(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_38,axiom,
product2(X1,X1,X1),
product2_idempotence ).
cnf(c_0_39,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_40,plain,
~ product1(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_41,plain,
product1(e_1,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_21])]) ).
cnf(c_0_42,plain,
( product1(e_3,e_2,e_1)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_43,plain,
~ product1(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_44,plain,
product1(e_3,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_21])]) ).
cnf(c_0_45,plain,
~ product2(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( product2(X4,X1,X2)
| ~ product1(X1,X2,X3)
| ~ product1(X3,X2,X4) ),
qg1a ).
cnf(c_0_47,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
~ product1(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_49,plain,
( product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
~ product1(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( ~ product1(X1,e_2,e_3)
| ~ product1(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
product1(e_1,e_2,e_3),
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
product1(e_3,e_2,e_1),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n024.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 21:25:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.18/0.57 % Version : CSE_E---1.5
% 0.18/0.57 % Problem : theBenchmark.p
% 0.18/0.57 % Proof found
% 0.18/0.57 % SZS status Theorem for theBenchmark.p
% 0.18/0.57 % SZS output start Proof
% See solution above
% 0.18/0.58 % Total time : 0.010000 s
% 0.18/0.58 % SZS output end Proof
% 0.18/0.58 % Total time : 0.013000 s
%------------------------------------------------------------------------------