%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-7.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:27:38 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 106 ( 44 unt; 0 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 85 ~; 112 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% 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 : 71 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_14,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_3]) ).
fof(product1_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product1(VAR_0,VAR_3,VAR_2)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_right_cancellation) ).
cnf(c_16,plain,
( equalish(B,D)
| ~ product1(A,D,C)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_right_cancellation]) ).
fof(product1_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product1(VAR_3,VAR_1,VAR_2)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_left_cancellation) ).
cnf(c_17,plain,
( equalish(A,D)
| ~ product1(D,B,C)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_left_cancellation]) ).
fof(product2_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product2(VAR_0,VAR_1,VAR_3)
| ~ product2(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product2_total_function2) ).
cnf(c_18,plain,
( equalish(C,D)
| ~ product2(A,B,D)
| ~ product2(A,B,C) ),
inference(clausify,[status(thm)],[product2_total_function2]) ).
fof(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_21,plain,
~ equalish(e_4,e_2),
inference(clausify,[status(thm)],[e_4_is_not_e_2]) ).
fof(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('theBenchmark.p',e_4_is_not_e_1) ).
cnf(c_22,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_is_not_e_1]) ).
fof(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_24,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_25,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_is_not_e_1]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_28,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_35,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_2,A,B) ),
inference(resolve,[status(thm)],[c_28,c_17]) ).
cnf(c_36,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_2,B) ),
inference(resolve,[status(thm)],[c_28,c_16]) ).
cnf(c_41,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_25,c_17]) ).
cnf(c_42,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_25,c_16]) ).
cnf(c_46,plain,
( ~ product2(A,B,e_2)
| ~ product2(A,B,e_3) ),
inference(resolve,[status(thm)],[c_24,c_18]) ).
cnf(c_47,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_24,c_17]) ).
cnf(c_48,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_53,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_22,c_17]) ).
cnf(c_59,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_60,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_21,c_16]) ).
cnf(c_65,plain,
( ~ product1(e_3,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_14,c_17]) ).
cnf(c_66,plain,
( ~ product1(A,e_3,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_16]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_68,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_69,plain,
group_element(e_2),
inference(clausify,[status(thm)],[element_2]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_70,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_71,plain,
group_element(e_4),
inference(clausify,[status(thm)],[element_4]) ).
fof(product1_total_function1,axiom,
! [VAR_0,VAR_1] :
( product1(VAR_0,VAR_1,e_4)
| product1(VAR_0,VAR_1,e_3)
| product1(VAR_0,VAR_1,e_2)
| product1(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product1_total_function1) ).
cnf(c_72,plain,
( product1(A,B,e_4)
| product1(A,B,e_3)
| product1(A,B,e_2)
| product1(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product1_total_function1]) ).
fof(product1_idempotence,axiom,
! [VAR_0] : product1(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product1_idempotence) ).
cnf(c_73,plain,
product1(A,A,A),
inference(clausify,[status(thm)],[product1_idempotence]) ).
fof(product2_idempotence,axiom,
! [VAR_0] : product2(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product2_idempotence) ).
cnf(c_75,plain,
product2(A,A,A),
inference(clausify,[status(thm)],[product2_idempotence]) ).
fof(qg2a,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product2(VAR_3,VAR_1,VAR_0)
| ~ product1(VAR_2,VAR_0,VAR_3)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2a) ).
cnf(c_76,plain,
( product2(D,B,A)
| ~ product1(C,A,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[qg2a]) ).
cnf(c_79,plain,
( product1(e_4,A,e_4)
| product1(e_4,A,e_3)
| product1(e_4,A,e_2)
| product1(e_4,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_72,c_71]) ).
cnf(c_80,plain,
( product1(e_3,A,e_4)
| product1(e_3,A,e_3)
| product1(e_3,A,e_2)
| product1(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_72,c_70]) ).
cnf(c_81,plain,
( product1(e_2,A,e_4)
| product1(e_2,A,e_3)
| product1(e_2,A,e_2)
| product1(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_72,c_69]) ).
cnf(c_82,plain,
( product1(e_1,A,e_4)
| product1(e_1,A,e_3)
| product1(e_1,A,e_2)
| product1(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_72,c_68]) ).
cnf(c_88,plain,
~ product1(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_73,c_66]) ).
cnf(c_91,plain,
~ product1(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_73,c_60]) ).
cnf(c_97,plain,
~ product1(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_73,c_48]) ).
cnf(c_98,plain,
~ product1(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_73,c_47]) ).
cnf(c_101,plain,
~ product1(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_73,c_41]) ).
cnf(c_104,plain,
~ product1(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_73,c_35]) ).
cnf(c_107,plain,
~ product1(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_65,c_73]) ).
cnf(c_110,plain,
~ product1(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_59,c_73]) ).
cnf(c_115,plain,
~ product1(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_48,c_73]) ).
cnf(c_116,plain,
~ product1(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_47,c_73]) ).
cnf(c_118,plain,
~ product1(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_42,c_73]) ).
cnf(c_121,plain,
~ product1(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_36,c_73]) ).
cnf(c_140,plain,
~ product2(e_3,e_3,e_2),
inference(resolve,[status(thm)],[c_75,c_46]) ).
cnf(c_158,plain,
~ product2(e_2,e_2,e_3),
inference(resolve,[status(thm)],[c_46,c_75]) ).
cnf(c_411,plain,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_79,c_70]) ).
cnf(c_412,plain,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_107,c_411]) ).
cnf(c_169,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_88,c_412]) ).
cnf(c_413,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_79,c_69]) ).
cnf(c_414,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_110,c_413]) ).
cnf(c_170,plain,
( product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_91,c_414]) ).
cnf(c_172,plain,
( product2(e_2,A,e_3)
| ~ product1(e_3,A,e_4)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_169,c_76]) ).
cnf(c_174,plain,
( ~ product1(e_1,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_169,c_53]) ).
cnf(c_176,plain,
( product2(e_3,A,e_2)
| ~ product1(e_2,A,e_4)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_170,c_76]) ).
cnf(c_178,plain,
( ~ product1(e_1,e_2,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_170,c_53]) ).
cnf(c_415,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_80,c_69]) ).
cnf(c_416,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_116,c_415]) ).
cnf(c_181,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_97,c_416]) ).
cnf(c_417,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_81,c_70]) ).
cnf(c_418,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_115,c_417]) ).
cnf(c_187,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_98,c_418]) ).
cnf(c_419,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_82,c_70]) ).
cnf(c_420,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_118,c_419]) ).
cnf(c_202,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_101,c_420]) ).
cnf(c_421,plain,
( product1(e_1,e_2,e_4)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_82,c_69]) ).
cnf(c_422,plain,
( product1(e_1,e_2,e_4)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_2) ),
inference(resolve,[status(thm)],[c_121,c_421]) ).
cnf(c_203,plain,
( product1(e_1,e_2,e_4)
| product1(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_104,c_422]) ).
cnf(c_224,plain,
( ~ product1(e_1,e_2,e_4)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_202,c_48]) ).
cnf(c_237,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_224,c_203]) ).
cnf(c_261,plain,
( product1(e_4,e_3,e_1)
| product1(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_237,c_174]) ).
cnf(c_292,plain,
( ~ product1(e_2,e_3,e_1)
| product1(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_261,c_59]) ).
cnf(c_293,plain,
( ~ product1(e_4,e_2,e_1)
| product1(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_261,c_48]) ).
cnf(c_423,plain,
( product1(e_3,e_2,e_1)
| product2(e_2,e_2,e_3)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_172,c_181]) ).
cnf(c_311,plain,
( product1(e_3,e_2,e_1)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_158,c_423]) ).
cnf(c_424,plain,
( product1(e_2,e_3,e_1)
| product2(e_3,e_3,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_176,c_187]) ).
cnf(c_326,plain,
( product1(e_2,e_3,e_1)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_140,c_424]) ).
cnf(c_343,plain,
( ~ product1(e_4,e_2,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_311,c_48]) ).
cnf(c_354,plain,
( product1(e_1,e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_326,c_293]) ).
cnf(c_358,plain,
( ~ product1(e_3,e_2,e_1)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_326,c_65]) ).
cnf(c_425,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_354,c_292]) ).
cnf(c_396,plain,
product1(e_1,e_2,e_3),
inference(copy,[status(thm)],[c_425]) ).
cnf(c_398,plain,
product1(e_4,e_2,e_1),
inference(resolve,[status(thm)],[c_396,c_178]) ).
cnf(c_401,plain,
product1(e_3,e_2,e_1),
inference(resolve,[status(thm)],[c_398,c_343]) ).
cnf(c_405,plain,
product1(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_401,c_358]) ).
cnf(c_426,plain,
( product2(e_3,A,e_2)
| ~ product1(e_2,A,e_1) ),
inference(resolve,[status(thm)],[c_76,c_396]) ).
cnf(c_427,plain,
~ product1(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_426,c_140]) ).
cnf(c_410,plain,
$false,
inference(resolve,[status(thm)],[c_405,c_427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-7.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:24:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2285416 was started by sandbox on n012,
% 0.13/0.36 % Fri Sep 25 14:24:50 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 72.
% 0.13/0.41 % Level of proof is 13.
% 0.13/0.41 % Maximum clause weight is 20.000.
% 0.13/0.41 % Given clauses 260.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
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