%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:27:40 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 40 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 156 ( 75 ~; 81 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(no_redundancy,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ greater(VAR_1,VAR_2)
| ~ next(VAR_0,VAR_2)
| ~ product(VAR_0,e_1,VAR_1) ),
file('theBenchmark.p',no_redundancy) ).
cnf(c_1,plain,
( ~ greater(B,C)
| ~ next(A,C)
| ~ product(A,e_1,B) ),
inference(clausify,[status(thm)],[no_redundancy]) ).
fof(e_2_then_e_3,axiom,
next(e_2,e_3),
file('theBenchmark.p',e_2_then_e_3) ).
cnf(c_3,plain,
next(e_2,e_3),
inference(clausify,[status(thm)],[e_2_then_e_3]) ).
fof(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('theBenchmark.p',e_4_greater_e_3) ).
cnf(c_5,plain,
greater(e_4,e_3),
inference(clausify,[status(thm)],[e_4_greater_e_3]) ).
cnf(c_7,plain,
( ~ greater(A,e_3)
| ~ product(e_2,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(product_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_total_function2) ).
cnf(c_14,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
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(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_16,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_17,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_19,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_23,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
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_27,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_28,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_29,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_31,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_33,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_28,c_16]) ).
cnf(c_34,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_35,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_38,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_27,c_17]) ).
cnf(c_39,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_27,c_16]) ).
cnf(c_40,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_27,c_15]) ).
cnf(c_43,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_14,c_19]) ).
fof(qg4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_1)
| ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg4) ).
cnf(c_47,plain,
( product(C,D,B)
| ~ product(B,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg4]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_48,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_49,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_50,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_51,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_52,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_53,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_54,plain,
~ product(e_2,e_1,e_4),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_67,plain,
~ product(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_48,c_40]) ).
cnf(c_72,plain,
~ product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_48,c_35]) ).
cnf(c_73,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_48,c_34]) ).
cnf(c_74,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_48,c_33]) ).
cnf(c_81,plain,
~ product(e_2,e_2,e_3),
inference(resolve,[status(thm)],[c_43,c_48]) ).
cnf(c_83,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_40,c_48]) ).
cnf(c_84,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_39,c_48]) ).
cnf(c_89,plain,
~ product(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_34,c_48]) ).
cnf(c_94,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_29,c_48]) ).
cnf(c_95,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_50,c_49]) ).
cnf(c_96,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_50,c_49]) ).
cnf(c_100,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_52,c_49]) ).
cnf(c_202,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_95,c_52]) ).
cnf(c_203,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_84,c_202]) ).
cnf(c_104,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_74,c_203]) ).
cnf(c_204,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_95,c_51]) ).
cnf(c_205,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_83,c_204]) ).
cnf(c_105,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_73,c_205]) ).
cnf(c_122,plain,
( ~ product(e_2,e_4,e_1)
| product(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_105,c_31]) ).
cnf(c_128,plain,
( product(e_2,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_122,c_104]) ).
cnf(c_145,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_128,c_38]) ).
cnf(c_206,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_96,c_51]) ).
cnf(c_207,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_89,c_206]) ).
cnf(c_156,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_67,c_207]) ).
cnf(c_208,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_100,c_53]) ).
cnf(c_209,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_94,c_208]) ).
cnf(c_210,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_72,c_209]) ).
cnf(c_176,plain,
product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_54,c_210]) ).
cnf(c_177,plain,
product(e_3,e_4,e_2),
inference(resolve,[status(thm)],[c_176,c_145]) ).
cnf(c_211,plain,
( product(A,e_2,e_3)
| ~ product(e_4,e_3,A) ),
inference(resolve,[status(thm)],[c_47,c_177]) ).
cnf(c_199,plain,
~ product(e_4,e_3,e_2),
inference(resolve,[status(thm)],[c_211,c_81]) ).
cnf(c_212,plain,
( product(e_2,A,e_4)
| ~ product(e_4,e_3,A) ),
inference(resolve,[status(thm)],[c_47,c_177]) ).
cnf(c_200,plain,
~ product(e_4,e_3,e_1),
inference(resolve,[status(thm)],[c_212,c_54]) ).
cnf(c_213,plain,
product(e_4,e_3,e_2),
inference(resolve,[status(thm)],[c_200,c_156]) ).
cnf(c_201,plain,
$false,
inference(resolve,[status(thm)],[c_199,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n004.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Fri Sep 25 14:26:26 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.44 % Process 3371015 was started by sandbox2 on n004,
% 0.17/5.44 % Fri Sep 25 14:26:26 2026
% 0.17/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.44
% 0.17/5.44 % From the command line: assign(max_seconds, 300).
% 0.17/5.47
% 0.17/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.47
% 0.17/5.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/5.47 % Length of proof is 52.
% 0.17/5.47 % Level of proof is 9.
% 0.17/5.47 % Maximum clause weight is 25.000.
% 0.17/5.47 % Given clauses 96.
% 0.17/5.47
% 0.17/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------