%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP130-1.003 : 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 : n018.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 0.37s 0.55s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 19 unt; 0 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 202 ( 54 ~; 148 |; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 47 ( 0 sgn 14 !; 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_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_2,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_3,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_5,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_8,plain,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
cnf(c_13,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_14,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_15,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_16,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
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_19,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_20,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_21,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_22,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_23,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_24,plain,
( product(B,B,A)
| ~ product(A,B,B) ),
inference(factor,[status(thm)],[c_19]) ).
cnf(c_25,plain,
( product(A,A,e_3)
| product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_20]) ).
cnf(c_26,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_21,c_20]) ).
cnf(c_28,plain,
( product(A,e_2,e_3)
| product(A,e_2,e_2)
| product(A,e_2,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_29,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_22,c_20]) ).
cnf(c_33,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_35,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_26,c_23]) ).
cnf(c_36,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_26,c_22]) ).
cnf(c_41,plain,
( product(A,e_2,e_2)
| ~ product(e_2,e_3,A)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_33,c_19]) ).
cnf(c_44,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_51,plain,
( ~ product(e_1,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_35,c_15]) ).
cnf(c_58,plain,
( ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_36,c_15]) ).
cnf(c_59,plain,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_36,c_14]) ).
cnf(c_61,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_67,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_29,c_23]) ).
cnf(c_86,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_58,c_33]) ).
cnf(c_88,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_61,c_51]) ).
cnf(c_91,plain,
( product(A,e_2,e_1)
| ~ product(e_1,e_3,A)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_61,c_19]) ).
cnf(c_93,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factor,[status(thm)],[c_91]) ).
cnf(c_94,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_67,c_59]) ).
cnf(c_97,plain,
( product(A,e_1,e_2)
| ~ product(e_2,e_3,A)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_67,c_19]) ).
cnf(c_99,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factor,[status(thm)],[c_97]) ).
cnf(c_393,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_86,c_44]) ).
cnf(c_394,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_393]) ).
cnf(c_132,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_394]) ).
cnf(c_395,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_132,c_41]) ).
cnf(c_396,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_395]) ).
cnf(c_140,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_396]) ).
cnf(c_146,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_140,c_13]) ).
cnf(c_150,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_88,c_14]) ).
cnf(c_397,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_94,c_99]) ).
cnf(c_398,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_397]) ).
cnf(c_153,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_398]) ).
cnf(c_399,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_97,c_153]) ).
cnf(c_400,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_399]) ).
cnf(c_161,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_400]) ).
cnf(c_170,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_161,c_146]) ).
cnf(c_173,plain,
( product(A,e_1,e_2)
| ~ product(e_2,e_2,A)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_161,c_19]) ).
cnf(c_174,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factor,[status(thm)],[c_173]) ).
cnf(c_401,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_170,c_174]) ).
cnf(c_402,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_401]) ).
cnf(c_294,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_402]) ).
cnf(c_403,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_294,c_24]) ).
cnf(c_295,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(copy,[status(thm)],[c_403]) ).
cnf(c_296,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_295,c_24]) ).
cnf(c_404,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_296,c_174]) ).
cnf(c_304,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(copy,[status(thm)],[c_404]) ).
cnf(c_405,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_304,c_24]) ).
cnf(c_309,plain,
product(e_1,e_1,e_2),
inference(copy,[status(thm)],[c_405]) ).
cnf(c_313,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_309,c_150]) ).
cnf(c_317,plain,
~ product(e_1,e_1,e_1),
inference(resolve,[status(thm)],[c_309,c_16]) ).
cnf(c_320,plain,
~ product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_13,c_309]) ).
cnf(c_352,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_320,c_313]) ).
cnf(c_360,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_320,c_93]) ).
cnf(c_406,plain,
( product(A,e_1,e_1)
| ~ product(e_1,e_2,A) ),
inference(resolve,[status(thm)],[c_19,c_309]) ).
cnf(c_381,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_406,c_317]) ).
cnf(c_385,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_381,c_360]) ).
cnf(c_407,plain,
product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_381,c_352]) ).
cnf(c_392,plain,
$false,
inference(resolve,[status(thm)],[c_385,c_407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.40 % Computer : n018.cluster.edu
% 0.07/0.40 % Model : x86_64 x86_64
% 0.07/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.40 % Memory : 8046.5625MB
% 0.07/0.40 % OS : Linux 6.8.0-71-generic
% 0.07/0.40 % CPULimit : 300
% 0.07/0.40 % WCLimit : 300
% 0.07/0.40 % DateTime : Fri Sep 25 14:31:20 UTC 2026
% 0.07/0.40 % CPUTime :
% 0.07/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.40 % Process 2168767 was started by sandbox on n018,
% 0.07/0.40 % Fri Sep 25 14:31:20 2026
% 0.07/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.41
% 0.07/0.41 % From the command line: assign(max_seconds, 300).
% 0.37/0.55
% 0.37/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.37/0.55
% 0.37/0.55 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.37/0.55 % Length of proof is 58.
% 0.37/0.55 % Level of proof is 17.
% 0.37/0.55 % Maximum clause weight is 16.000.
% 0.37/0.55 % Given clauses 163.
% 0.37/0.55
% 0.37/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------