%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP127-1.004 : 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 : n008.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 104 ( 44 unt; 0 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 187 ( 79 ~; 108 |; 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 : 57 ( 0 sgn 15 !; 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_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_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_6,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_7,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_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_17,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_18,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
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_21,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_23,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_24,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
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]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_3,VAR_0,VAR_1)
| ~ product(VAR_2,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_34,plain,
( product(D,A,B)
| ~ product(C,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
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_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_38,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_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]) ).
cnf(c_56,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_35,c_27]) ).
cnf(c_58,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_35,c_26]) ).
cnf(c_59,plain,
~ product(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_35,c_26]) ).
cnf(c_60,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_35,c_25]) ).
cnf(c_61,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_35,c_25]) ).
cnf(c_62,plain,
~ product(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_35,c_24]) ).
cnf(c_63,plain,
~ product(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_35,c_24]) ).
cnf(c_64,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_35,c_23]) ).
cnf(c_65,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_35,c_23]) ).
cnf(c_69,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_21]) ).
cnf(c_71,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_20]) ).
cnf(c_73,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_19]) ).
cnf(c_74,plain,
~ product(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_35,c_18]) ).
cnf(c_75,plain,
~ product(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_35,c_18]) ).
cnf(c_76,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_35,c_17]) ).
cnf(c_77,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_35,c_17]) ).
cnf(c_80,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_82,plain,
( product(A,e_3,e_4)
| product(A,e_3,e_3)
| product(A,e_3,e_2)
| product(A,e_3,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_38,c_36]) ).
cnf(c_83,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_38,c_36]) ).
cnf(c_262,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_80,c_40]) ).
cnf(c_263,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_60,c_262]) ).
cnf(c_88,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_73,c_263]) ).
cnf(c_264,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_80,c_39]) ).
cnf(c_265,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_58,c_264]) ).
cnf(c_89,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_71,c_265]) ).
cnf(c_266,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_80,c_38]) ).
cnf(c_267,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_56,c_266]) ).
cnf(c_90,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_69,c_267]) ).
cnf(c_92,plain,
( product(A,e_1,e_4)
| ~ product(e_3,e_1,A)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_88,c_34]) ).
cnf(c_94,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_88,c_16]) ).
cnf(c_96,plain,
( product(A,e_2,e_4)
| ~ product(e_3,e_2,A)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_89,c_34]) ).
cnf(c_101,plain,
( ~ product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_90,c_25]) ).
cnf(c_102,plain,
( ~ product(e_1,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_90,c_17]) ).
cnf(c_103,plain,
( product(e_2,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_94,c_89]) ).
cnf(c_107,plain,
( ~ product(e_3,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_103,c_18]) ).
cnf(c_268,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_82,c_40]) ).
cnf(c_269,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_64,c_268]) ).
cnf(c_125,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_77,c_269]) ).
cnf(c_270,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_82,c_39]) ).
cnf(c_271,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_62,c_270]) ).
cnf(c_126,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_75,c_271]) ).
cnf(c_272,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_83,c_40]) ).
cnf(c_273,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_76,c_272]) ).
cnf(c_127,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_65,c_273]) ).
cnf(c_274,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_83,c_39]) ).
cnf(c_275,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_74,c_274]) ).
cnf(c_128,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_63,c_275]) ).
cnf(c_143,plain,
( ~ product(e_2,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_125,c_16]) ).
cnf(c_276,plain,
( product(e_4,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_127,c_92]) ).
cnf(c_149,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_61,c_276]) ).
cnf(c_277,plain,
( product(e_3,e_2,e_1)
| product(e_4,e_2,e_4)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_96,c_128]) ).
cnf(c_163,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_59,c_277]) ).
cnf(c_167,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_143,c_126]) ).
cnf(c_176,plain,
( product(e_3,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_149,c_101]) ).
cnf(c_197,plain,
( ~ product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_163,c_26]) ).
cnf(c_222,plain,
( ~ product(e_2,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_167,c_27]) ).
cnf(c_278,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_176,c_107]) ).
cnf(c_248,plain,
product(e_1,e_4,e_2),
inference(copy,[status(thm)],[c_278]) ).
cnf(c_250,plain,
product(e_3,e_4,e_1),
inference(resolve,[status(thm)],[c_248,c_102]) ).
cnf(c_252,plain,
product(e_2,e_4,e_1),
inference(resolve,[status(thm)],[c_250,c_197]) ).
cnf(c_254,plain,
product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_252,c_222]) ).
cnf(c_279,plain,
~ product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_248,c_27]) ).
cnf(c_261,plain,
$false,
inference(resolve,[status(thm)],[c_254,c_279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP127-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 14:27:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1263199 was started by sandbox on n008,
% 0.10/0.36 % Fri Sep 25 14:27:24 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 71.
% 0.14/0.40 % Level of proof is 11.
% 0.14/0.40 % Maximum clause weight is 25.000.
% 0.14/0.40 % Given clauses 148.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------