%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP134-2.003 : 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 : n007.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 07:28:05 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 23 unt; 0 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 174 ( 65 ~; 109 |; 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 : 60 ( 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_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_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
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]) ).
cnf(c_25,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
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_27,plain,
( product(C,D,B)
| ~ product(B,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg4]) ).
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_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,A,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_41,plain,
~ product(e_3,e_3,e_1),
inference(resolve,[status(thm)],[c_33,c_32]) ).
cnf(c_319,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_319]) ).
cnf(c_320,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_44,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_41,c_320]) ).
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_47,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_42,c_33]) ).
cnf(c_53,plain,
( ~ product(e_3,e_1,e_3)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_44,c_22]) ).
cnf(c_55,plain,
( ~ product(e_1,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_44,c_19]) ).
cnf(c_57,plain,
( product(e_1,A,e_2)
| ~ product(e_2,e_2,A)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_47,c_27]) ).
cnf(c_60,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_68,plain,
( product(e_3,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_45,c_55]) ).
cnf(c_69,plain,
( product(A,e_3,e_1)
| ~ product(e_3,e_1,A)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_45,c_27]) ).
cnf(c_81,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_60,c_53]) ).
cnf(c_102,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_68,c_33]) ).
cnf(c_106,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_68,c_22]) ).
cnf(c_321,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| 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_69,c_60]) ).
cnf(c_116,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_41,c_321]) ).
cnf(c_121,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_81,c_33]) ).
cnf(c_126,plain,
( ~ product(e_1,e_3,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_81,c_19]) ).
cnf(c_322,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_102,c_57]) ).
cnf(c_138,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_322]) ).
cnf(c_153,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_121,c_19]) ).
cnf(c_167,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_138,c_22]) ).
cnf(c_172,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_153,c_42]) ).
cnf(c_323,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_167,c_42]) ).
cnf(c_174,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_323]) ).
cnf(c_176,plain,
( product(A,e_1,e_1)
| ~ product(e_3,e_1,A)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_174,c_27]) ).
cnf(c_178,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(factor,[status(thm)],[c_176]) ).
cnf(c_324,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3) ),
inference(resolve,[status(thm)],[c_172,c_178]) ).
cnf(c_184,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3) ),
inference(copy,[status(thm)],[c_324]) ).
cnf(c_198,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_184,c_25]) ).
cnf(c_325,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_198,c_47]) ).
cnf(c_215,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_325]) ).
cnf(c_218,plain,
~ product(e_1,e_1,e_2),
inference(resolve,[status(thm)],[c_24,c_215]) ).
cnf(c_219,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_22,c_215]) ).
cnf(c_221,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_19,c_215]) ).
cnf(c_326,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_219,c_116]) ).
cnf(c_230,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_221,c_326]) ).
cnf(c_234,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_219,c_106]) ).
cnf(c_262,plain,
( ~ product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_221,c_126]) ).
cnf(c_278,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_33,c_218]) ).
cnf(c_327,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_234,c_230]) ).
cnf(c_307,plain,
product(e_1,e_3,e_2),
inference(copy,[status(thm)],[c_327]) ).
cnf(c_309,plain,
product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_307,c_262]) ).
cnf(c_328,plain,
( product(A,e_2,e_1)
| ~ product(e_3,e_1,A) ),
inference(resolve,[status(thm)],[c_27,c_307]) ).
cnf(c_329,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_328,c_278]) ).
cnf(c_318,plain,
$false,
inference(resolve,[status(thm)],[c_309,c_329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP134-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:28:39 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1206411 was started by sandbox2 on n007,
% 0.17/0.44 % Fri Sep 25 14:28:39 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.51
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.51
% 0.17/0.51 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.17/0.51 % Length of proof is 59.
% 0.17/0.51 % Level of proof is 20.
% 0.17/0.51 % Maximum clause weight is 16.000.
% 0.17/0.51 % Given clauses 146.
% 0.17/0.51
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------