%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-3.004 : 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 : n019.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 07:27:37 AM UTC 2026
% Result : Unsatisfiable 0.81s 0.47s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of formulae : 136 ( 58 unt; 0 def)
% Number of atoms : 308 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 338 ( 166 ~; 172 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 110 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cycle7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ next(VAR_0,VAR_3)
| ~ greater(VAR_1,e_0)
| ~ product(VAR_0,e_1,VAR_2)
| ~ cycle(VAR_0,VAR_1) ),
file('theBenchmark.p',cycle7) ).
cnf(c_2,plain,
( equalish(C,D)
| ~ next(A,D)
| ~ greater(B,e_0)
| ~ product(A,e_1,C)
| ~ cycle(A,B) ),
inference(clausify,[status(thm)],[cycle7]) ).
fof(cycle4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( equalish(VAR_1,VAR_4)
| ~ next(VAR_3,VAR_4)
| ~ greater(VAR_1,e_0)
| ~ next(VAR_0,VAR_2)
| ~ cycle(VAR_2,VAR_3)
| ~ cycle(VAR_0,VAR_1) ),
file('theBenchmark.p',cycle4) ).
cnf(c_3,plain,
( equalish(B,E)
| ~ next(D,E)
| ~ greater(B,e_0)
| ~ next(A,C)
| ~ cycle(C,D)
| ~ cycle(A,B) ),
inference(clausify,[status(thm)],[cycle4]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_7,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('theBenchmark.p',e_2_is_not_e_4) ).
cnf(c_9,plain,
~ equalish(e_2,e_4),
inference(clausify,[status(thm)],[e_2_is_not_e_4]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_10,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_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_11,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_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_13,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_is_not_e_1]) ).
fof(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_14,plain,
~ equalish(e_4,e_2),
inference(clausify,[status(thm)],[e_4_is_not_e_2]) ).
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_15,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_3]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_17,plain,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
fof(product_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_3,VAR_1,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(c_18,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
fof(qg2_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_1,VAR_4)
| ~ product(VAR_5,VAR_3,VAR_4)
| ~ product(VAR_5,VAR_0,VAR_1)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2_2) ).
cnf(c_20,plain,
( equalish(B,E)
| ~ product(F,D,E)
| ~ product(F,A,B)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg2_2]) ).
cnf(c_22,plain,
( ~ product(D,C,e_1)
| ~ product(D,A,e_3)
| ~ product(C,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_24,plain,
( ~ product(D,C,e_1)
| ~ product(D,A,e_4)
| ~ product(C,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_33,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_18,c_7]) ).
cnf(c_34,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_10]) ).
cnf(c_35,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_36,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_37,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_38,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_39,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_40,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_17,c_10]) ).
cnf(c_42,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_44,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_62,plain,
( ~ next(C,e_1)
| ~ greater(e_3,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_10,c_3]) ).
cnf(c_66,plain,
( ~ next(A,e_4)
| ~ greater(B,e_0)
| ~ product(A,e_1,e_2)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_70,plain,
( ~ next(C,e_1)
| ~ greater(e_2,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_81,plain,
product(A,A,A),
inference(clausify,[status(thm)],[product_idempotence]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,e_4)
| product(VAR_0,VAR_1,e_3)
| product(VAR_0,VAR_1,e_2)
| product(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product_total_function1) ).
cnf(c_82,plain,
( product(A,B,e_4)
| product(A,B,e_3)
| product(A,B,e_2)
| product(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product_total_function1]) ).
fof(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_83,plain,
group_element(e_4),
inference(clausify,[status(thm)],[element_4]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_84,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_85,plain,
group_element(e_2),
inference(clausify,[status(thm)],[element_2]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_86,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(cycle6,axiom,
! [VAR_0,VAR_1] :
( ~ greater(VAR_1,VAR_0)
| ~ product(VAR_0,e_1,VAR_1)
| ~ cycle(VAR_0,e_0) ),
file('theBenchmark.p',cycle6) ).
cnf(c_87,plain,
( ~ greater(B,A)
| ~ product(A,e_1,B)
| ~ cycle(A,e_0) ),
inference(clausify,[status(thm)],[cycle6]) ).
fof(cycle3,axiom,
cycle(e_4,e_0),
file('theBenchmark.p',cycle3) ).
cnf(c_89,plain,
cycle(e_4,e_0),
inference(clausify,[status(thm)],[cycle3]) ).
fof(cycle2,axiom,
! [VAR_0] :
( cycle(VAR_0,e_3)
| cycle(VAR_0,e_2)
| cycle(VAR_0,e_1)
| cycle(VAR_0,e_0)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',cycle2) ).
cnf(c_90,plain,
( cycle(A,e_3)
| cycle(A,e_2)
| cycle(A,e_1)
| cycle(A,e_0)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[cycle2]) ).
fof(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('theBenchmark.p',e_4_greater_e_3) ).
cnf(c_91,plain,
greater(e_4,e_3),
inference(clausify,[status(thm)],[e_4_greater_e_3]) ).
fof(e_3_greater_e_0,axiom,
greater(e_3,e_0),
file('theBenchmark.p',e_3_greater_e_0) ).
cnf(c_98,plain,
greater(e_3,e_0),
inference(clausify,[status(thm)],[e_3_greater_e_0]) ).
fof(e_2_greater_e_0,axiom,
greater(e_2,e_0),
file('theBenchmark.p',e_2_greater_e_0) ).
cnf(c_99,plain,
greater(e_2,e_0),
inference(clausify,[status(thm)],[e_2_greater_e_0]) ).
fof(e_1_greater_e_0,axiom,
greater(e_1,e_0),
file('theBenchmark.p',e_1_greater_e_0) ).
cnf(c_100,plain,
greater(e_1,e_0),
inference(clausify,[status(thm)],[e_1_greater_e_0]) ).
fof(e_3_then_e_4,axiom,
next(e_3,e_4),
file('theBenchmark.p',e_3_then_e_4) ).
cnf(c_101,plain,
next(e_3,e_4),
inference(clausify,[status(thm)],[e_3_then_e_4]) ).
fof(e_0_then_e_1,axiom,
next(e_0,e_1),
file('theBenchmark.p',e_0_then_e_1) ).
cnf(c_104,plain,
next(e_0,e_1),
inference(clausify,[status(thm)],[e_0_then_e_1]) ).
cnf(c_182,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_98,c_62]) ).
cnf(c_185,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_99,c_70]) ).
cnf(c_203,plain,
~ product(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_81,c_44]) ).
cnf(c_205,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_81,c_42]) ).
cnf(c_207,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_81,c_40]) ).
cnf(c_208,plain,
~ product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_81,c_39]) ).
cnf(c_209,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_81,c_38]) ).
cnf(c_248,plain,
( ~ product(e_4,B,e_1)
| ~ product(B,e_1,A)
| ~ product(e_4,e_4,A) ),
inference(resolve,[status(thm)],[c_81,c_24]) ).
cnf(c_258,plain,
( ~ product(B,A,e_1)
| ~ product(B,e_3,e_3)
| ~ product(A,e_1,e_3) ),
inference(resolve,[status(thm)],[c_81,c_22]) ).
cnf(c_269,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_44,c_81]) ).
cnf(c_275,plain,
~ product(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_38,c_81]) ).
cnf(c_277,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_36,c_81]) ).
cnf(c_279,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_34,c_81]) ).
cnf(c_280,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_33,c_81]) ).
cnf(c_281,plain,
( product(A,e_4,e_4)
| product(A,e_4,e_3)
| product(A,e_4,e_2)
| product(A,e_4,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_83,c_82]) ).
cnf(c_282,plain,
( product(e_4,A,e_4)
| product(e_4,A,e_3)
| product(e_4,A,e_2)
| product(e_4,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_83,c_82]) ).
cnf(c_284,plain,
( product(e_3,A,e_4)
| product(e_3,A,e_3)
| product(e_3,A,e_2)
| product(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_84,c_82]) ).
cnf(c_286,plain,
( product(e_2,A,e_4)
| product(e_2,A,e_3)
| product(e_2,A,e_2)
| product(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_85,c_82]) ).
cnf(c_292,plain,
( cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_90,c_84]) ).
cnf(c_787,plain,
( ~ next(e_0,e_1)
| ~ next(A,e_4)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_182,c_89]) ).
cnf(c_788,plain,
( ~ next(e_0,e_1)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_787,c_101]) ).
cnf(c_338,plain,
~ cycle(e_3,e_3),
inference(resolve,[status(thm)],[c_788,c_104]) ).
cnf(c_339,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_338,c_292]) ).
cnf(c_789,plain,
( ~ next(e_0,e_1)
| ~ next(A,e_4)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_185,c_89]) ).
cnf(c_790,plain,
( ~ next(e_0,e_1)
| ~ cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_789,c_101]) ).
cnf(c_347,plain,
~ cycle(e_3,e_2),
inference(resolve,[status(thm)],[c_790,c_104]) ).
cnf(c_348,plain,
( cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_347,c_339]) ).
cnf(c_791,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_281,c_84]) ).
cnf(c_792,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_269,c_791]) ).
cnf(c_368,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_209,c_792]) ).
cnf(c_402,plain,
( ~ product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_368,c_42]) ).
cnf(c_793,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolve,[status(thm)],[c_282,c_86]) ).
cnf(c_794,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_277,c_793]) ).
cnf(c_455,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_205,c_794]) ).
cnf(c_795,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_282,c_84]) ).
cnf(c_796,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_275,c_795]) ).
cnf(c_457,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_203,c_796]) ).
cnf(c_797,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_284,c_86]) ).
cnf(c_798,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_279,c_797]) ).
cnf(c_460,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_207,c_798]) ).
cnf(c_477,plain,
( ~ product(e_2,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_455,c_37]) ).
cnf(c_523,plain,
( ~ product(e_4,e_1,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_457,c_40]) ).
cnf(c_799,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_286,c_86]) ).
cnf(c_800,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_280,c_799]) ).
cnf(c_577,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_208,c_800]) ).
cnf(c_801,plain,
( ~ product(e_4,e_3,e_1)
| ~ product(e_4,e_4,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_460,c_248]) ).
cnf(c_588,plain,
( ~ product(e_4,e_3,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_81,c_801]) ).
cnf(c_802,plain,
( ~ greater(e_4,e_3)
| ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_460,c_87]) ).
cnf(c_591,plain,
( ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_91,c_802]) ).
cnf(c_595,plain,
( ~ product(e_2,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_460,c_35]) ).
cnf(c_608,plain,
( cycle(e_3,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_591,c_348]) ).
cnf(c_609,plain,
( product(e_3,e_4,e_1)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_608,c_402]) ).
cnf(c_803,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_4,e_1,e_3)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_609,c_258]) ).
cnf(c_631,plain,
( ~ product(e_4,e_1,e_3)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_81,c_803]) ).
cnf(c_655,plain,
( product(e_4,e_1,e_2)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_631,c_455]) ).
cnf(c_665,plain,
( ~ product(e_3,e_1,e_2)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_655,c_38]) ).
cnf(c_804,plain,
( cycle(e_3,e_1)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_665,c_608]) ).
cnf(c_712,plain,
cycle(e_3,e_1),
inference(copy,[status(thm)],[c_804]) ).
cnf(c_805,plain,
( ~ next(e_3,e_4)
| ~ greater(e_1,e_0)
| ~ product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_66,c_712]) ).
cnf(c_806,plain,
( ~ next(e_3,e_4)
| ~ product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_805,c_100]) ).
cnf(c_739,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_806,c_101]) ).
cnf(c_752,plain,
~ product(e_2,e_1,e_4),
inference(resolve,[status(thm)],[c_739,c_595]) ).
cnf(c_758,plain,
~ product(e_4,e_3,e_1),
inference(resolve,[status(thm)],[c_739,c_588]) ).
cnf(c_763,plain,
product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_752,c_577]) ).
cnf(c_777,plain,
~ product(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_758,c_523]) ).
cnf(c_807,plain,
~ product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_777,c_477]) ).
cnf(c_786,plain,
$false,
inference(resolve,[status(thm)],[c_763,c_807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:25:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2955558 was started by sandbox on n019,
% 0.09/0.35 % Fri Sep 25 14:25:33 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.81/0.47
% 0.81/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.81/0.47
% 0.81/0.47 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.81/0.47 % Length of proof is 88.
% 0.81/0.47 % Level of proof is 15.
% 0.81/0.47 % Maximum clause weight is 25.000.
% 0.81/0.47 % Given clauses 389.
% 0.81/0.47
% 0.81/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------