%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.16s 0.52s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 31 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 72 ~; 89 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 70 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_2,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_3,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_4,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_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_10,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_14,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_15,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_16,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_20,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_22,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_25,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_26,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_27,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
cnf(c_28,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_33,plain,
( ~ product(A,B,e_3)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
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_34,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_35,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_36,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_37,plain,
group_element(e_4),
inference(clausify,[status(thm)],[element_4]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_39,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_40,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(qg4_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_2,VAR_3,VAR_1)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg4_1) ).
cnf(c_42,plain,
( ~ product(B,A,D)
| ~ product(C,D,B)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg4_1]) ).
cnf(c_56,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_35,c_28]) ).
cnf(c_58,plain,
~ product(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_35,c_26]) ).
cnf(c_59,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_35,c_25]) ).
cnf(c_64,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_20]) ).
cnf(c_65,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_19]) ).
cnf(c_69,plain,
~ product(e_3,e_3,e_4),
inference(resolve,[status(thm)],[c_33,c_35]) ).
cnf(c_76,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_26,c_35]) ).
cnf(c_77,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_25,c_35]) ).
cnf(c_82,plain,
~ product(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_20,c_35]) ).
cnf(c_83,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_19,c_35]) ).
cnf(c_87,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_37,c_36]) ).
cnf(c_88,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_37,c_36]) ).
cnf(c_247,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(resolve,[status(thm)],[c_87,c_40]) ).
cnf(c_248,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_77,c_247]) ).
cnf(c_115,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_65,c_248]) ).
cnf(c_249,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_87,c_39]) ).
cnf(c_250,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_76,c_249]) ).
cnf(c_116,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_64,c_250]) ).
cnf(c_122,plain,
( product(A,e_3,e_1)
| ~ product(e_4,e_1,A)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_115,c_34]) ).
cnf(c_123,plain,
( product(e_3,A,e_4)
| ~ product(e_4,e_1,A)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_115,c_34]) ).
cnf(c_132,plain,
( ~ product(e_1,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_116,c_16]) ).
cnf(c_141,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_132,c_115]) ).
cnf(c_148,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_141,c_27]) ).
cnf(c_251,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_88,c_40]) ).
cnf(c_252,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_83,c_251]) ).
cnf(c_149,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_59,c_252]) ).
cnf(c_253,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_88,c_39]) ).
cnf(c_254,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_82,c_253]) ).
cnf(c_150,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_58,c_254]) ).
cnf(c_255,plain,
( product(e_3,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_149,c_123]) ).
cnf(c_152,plain,
( product(e_1,e_4,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_69,c_255]) ).
cnf(c_168,plain,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_150,c_22]) ).
cnf(c_256,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_152,c_122]) ).
cnf(c_180,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(copy,[status(thm)],[c_256]) ).
cnf(c_208,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_168,c_149]) ).
cnf(c_257,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_180,c_148]) ).
cnf(c_230,plain,
product(e_1,e_4,e_2),
inference(copy,[status(thm)],[c_257]) ).
cnf(c_258,plain,
( ~ product(e_1,e_4,A)
| ~ product(e_4,A,e_1) ),
inference(resolve,[status(thm)],[c_42,c_59]) ).
cnf(c_239,plain,
~ product(e_4,e_2,e_1),
inference(resolve,[status(thm)],[c_258,c_230]) ).
cnf(c_259,plain,
( product(A,e_2,e_1)
| ~ product(e_4,e_1,A) ),
inference(resolve,[status(thm)],[c_34,c_230]) ).
cnf(c_241,plain,
~ product(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_259,c_56]) ).
cnf(c_260,plain,
product(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_239,c_208]) ).
cnf(c_246,plain,
$false,
inference(resolve,[status(thm)],[c_241,c_260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n011.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 14:26:59 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2218843 was started by sandbox2 on n011,
% 0.16/0.44 % Fri Sep 25 14:26:59 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.52
% 0.16/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52
% 0.16/0.52 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.16/0.52 % Length of proof is 52.
% 0.16/0.52 % Level of proof is 9.
% 0.16/0.52 % Maximum clause weight is 20.000.
% 0.16/0.52 % Given clauses 121.
% 0.16/0.52
% 0.16/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------