TSTP Solution File: GRP131-2.002 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP131-2.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 00:17:10 EDT 2023
% Result : Unsatisfiable 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 12 unt; 7 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 125 ( 59 ~; 66 |; 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 : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 50 ( 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,
greater: ( $i * $i ) > $o ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
group_element: $i > $o ).
tff(decl_28,type,
equalish: ( $i * $i ) > $o ).
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
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(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
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(qg1_2,negated_conjecture,
( equalish(X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X2,X1)
| ~ product(X6,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
cnf(c_0_8,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_9,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_10,plain,
( product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_12,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_13,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_15,plain,
( equalish(X1,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_17,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_18,plain,
( product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( equalish(X1,e_2)
| product(e_2,e_2,e_1)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_20,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_21,plain,
( equalish(X1,e_1)
| ~ product(e_1,e_1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( equalish(X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X2,X1)
| ~ product(X6,X5,X4) ),
qg1_2 ).
cnf(c_0_24,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_26,plain,
( equalish(X1,e_2)
| ~ product(e_2,e_1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_27,plain,
( equalish(X1,e_1)
| product(e_1,e_2,e_1)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_28,negated_conjecture,
( equalish(X1,e_2)
| product(e_2,e_2,e_1)
| ~ product(e_2,e_2,X2)
| ~ product(e_2,X1,X3)
| ~ product(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_29,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_30,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_9]) ).
cnf(c_0_31,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_32,plain,
( product(e_1,e_2,e_1)
| ~ product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( equalish(X1,e_2)
| product(e_2,e_2,e_1)
| ~ product(e_2,X1,X2)
| ~ product(X2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_34,plain,
( product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_2,e_2,X2)
| ~ product(e_1,X1,X3)
| ~ product(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_37,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_38,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_39,negated_conjecture,
~ product(e_1,e_1,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_14]),c_0_24]) ).
cnf(c_0_40,plain,
( equalish(X1,e_2)
| ~ product(e_1,e_2,e_1)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
product(e_1,e_1,e_1),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_14,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
product(e_1,e_2,e_1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_42])]),c_0_14]) ).
cnf(c_0_45,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_42])]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP131-2.002 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 21:12:47 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.52 start to proof: theBenchmark
% 0.18/0.54 % Version : CSE_E---1.5
% 0.18/0.54 % Problem : theBenchmark.p
% 0.18/0.54 % Proof found
% 0.18/0.54 % SZS status Theorem for theBenchmark.p
% 0.18/0.54 % SZS output start Proof
% See solution above
% 0.18/0.54 % Total time : 0.011000 s
% 0.18/0.54 % SZS output end Proof
% 0.18/0.54 % Total time : 0.014000 s
%------------------------------------------------------------------------------