%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP130-2.003 : 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 : n015.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 07:28:03 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 29 unt; 0 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 179 ( 68 ~; 111 |; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 63 ( 0 sgn 21 !; 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_1_then_e_2,axiom,
next(e_1,e_2),
file('theBenchmark.p',e_1_then_e_2) ).
cnf(c_3,plain,
next(e_1,e_2),
inference(clausify,[status(thm)],[e_1_then_e_2]) ).
fof(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('theBenchmark.p',e_3_greater_e_2) ).
cnf(c_4,plain,
greater(e_3,e_2),
inference(clausify,[status(thm)],[e_3_greater_e_2]) ).
cnf(c_6,plain,
( ~ greater(A,e_2)
| ~ product(e_1,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_9,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
fof(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_10,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_11,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_13,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_16,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_17,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_18,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_20,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_17,c_10]) ).
cnf(c_22,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_24,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_9,c_13]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_3,VAR_1,VAR_0)
| ~ product(VAR_0,VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_27,plain,
( product(D,B,A)
| ~ product(A,C,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( 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_28,plain,
( 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_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_29,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_30,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_31,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_32,plain,
~ product(e_1,e_1,e_3),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_33,plain,
( product(B,B,A)
| ~ product(A,B,B) ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_34,plain,
( product(A,A,e_3)
| product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_35,plain,
( 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_29,c_28]) ).
cnf(c_36,plain,
( 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_29,c_28]) ).
cnf(c_38,plain,
( 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_30,c_28]) ).
cnf(c_41,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_33,c_32]) ).
cnf(c_271,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_34,c_31]) ).
cnf(c_42,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_32,c_271]) ).
cnf(c_44,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_34,c_29]) ).
cnf(c_45,plain,
( 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_35,c_31]) ).
cnf(c_46,plain,
( 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_35,c_30]) ).
cnf(c_57,plain,
( ~ product(e_3,e_1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_44,c_22]) ).
cnf(c_272,plain,
( 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_36,c_31]) ).
cnf(c_58,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_41,c_272]) ).
cnf(c_61,plain,
( product(A,e_1,e_3)
| ~ product(e_3,e_3,A)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_58,c_27]) ).
cnf(c_62,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_58,c_20]) ).
cnf(c_63,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_45,c_33]) ).
cnf(c_67,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_46,c_33]) ).
cnf(c_74,plain,
( 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_38,c_31]) ).
cnf(c_75,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_57,c_58]) ).
cnf(c_273,plain,
( product(e_1,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_63,c_61]) ).
cnf(c_82,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_32,c_273]) ).
cnf(c_93,plain,
( ~ product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_67,c_19]) ).
cnf(c_274,plain,
( product(e_2,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_75,c_61]) ).
cnf(c_108,plain,
( product(e_2,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_117,plain,
( product(e_2,A,e_3)
| ~ product(e_3,A,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_82,c_27]) ).
cnf(c_275,plain,
( product(e_1,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_108,c_61]) ).
cnf(c_276,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_129,plain,
( product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_32,c_276]) ).
cnf(c_133,plain,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_129,c_20]) ).
cnf(c_134,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_129,c_19]) ).
cnf(c_136,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_134,c_42]) ).
cnf(c_138,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_136,c_62]) ).
cnf(c_146,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_138,c_19]) ).
cnf(c_277,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_146,c_42]) ).
cnf(c_147,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_149,plain,
~ product(e_1,e_1,e_2),
inference(resolve,[status(thm)],[c_24,c_147]) ).
cnf(c_150,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_22,c_147]) ).
cnf(c_152,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_18,c_147]) ).
cnf(c_155,plain,
( product(e_2,A,e_3)
| ~ product(e_3,A,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_150,c_117]) ).
cnf(c_166,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_150,c_63]) ).
cnf(c_167,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_150,c_45]) ).
cnf(c_181,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_152,c_74]) ).
cnf(c_278,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_155,c_166]) ).
cnf(c_214,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(copy,[status(thm)],[c_278]) ).
cnf(c_222,plain,
( ~ product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_214,c_18]) ).
cnf(c_279,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_222,c_167]) ).
cnf(c_233,plain,
product(e_1,e_3,e_2),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_237,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_233,c_93]) ).
cnf(c_247,plain,
~ product(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_18,c_233]) ).
cnf(c_257,plain,
product(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_247,c_237]) ).
cnf(c_280,plain,
( product(e_1,A,e_2)
| ~ product(e_2,A,e_3) ),
inference(resolve,[status(thm)],[c_27,c_257]) ).
cnf(c_264,plain,
~ product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_280,c_149]) ).
cnf(c_268,plain,
product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_264,c_181]) ).
cnf(c_281,plain,
~ product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_264,c_133]) ).
cnf(c_270,plain,
$false,
inference(resolve,[status(thm)],[c_268,c_281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 14:32:12 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 1586098 was started by sandbox on n015,
% 0.09/0.35 % Fri Sep 25 14:32:12 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).
% 0.14/0.37
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.37
% 0.14/0.37 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.37 % Length of proof is 66.
% 0.14/0.37 % Level of proof is 22.
% 0.14/0.37 % Maximum clause weight is 16.000.
% 0.14/0.37 % Given clauses 126.
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------