%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP126-3.004 : 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 : n017.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 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 93 ( 39 unt; 0 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 74 ~; 99 |; 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 : 64 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_7,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_10,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_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_11,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_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_13,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_is_not_e_1]) ).
fof(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_14,plain,
~ equalish(e_4,e_2),
inference(clausify,[status(thm)],[e_4_is_not_e_2]) ).
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_15,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_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_16,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
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_17,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_18,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_2,A,B) ),
inference(resolve,[status(thm)],[c_18,c_7]) ).
cnf(c_20,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_10]) ).
cnf(c_21,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_22,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_23,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_24,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_28,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_29,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_30,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_36,plain,
( ~ product(A,B,e_3)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
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_67,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_68,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_69,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_70,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_71,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_72,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_73,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_146,plain,
~ product(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_68,c_29]) ).
cnf(c_147,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_68,c_28]) ).
cnf(c_151,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_68,c_24]) ).
cnf(c_152,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_68,c_23]) ).
cnf(c_153,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_68,c_22]) ).
cnf(c_157,plain,
~ product(e_3,e_3,e_4),
inference(resolve,[status(thm)],[c_36,c_68]) ).
cnf(c_163,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_30,c_68]) ).
cnf(c_164,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_29,c_68]) ).
cnf(c_165,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_28,c_68]) ).
cnf(c_170,plain,
~ product(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_23,c_68]) ).
cnf(c_171,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_22,c_68]) ).
cnf(c_175,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_70,c_69]) ).
cnf(c_176,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_70,c_69]) ).
cnf(c_352,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_175,c_73]) ).
cnf(c_353,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_165,c_352]) ).
cnf(c_260,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_153,c_353]) ).
cnf(c_354,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_175,c_72]) ).
cnf(c_355,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_164,c_354]) ).
cnf(c_261,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_152,c_355]) ).
cnf(c_356,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_175,c_71]) ).
cnf(c_357,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_163,c_356]) ).
cnf(c_262,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_151,c_357]) ).
cnf(c_263,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_260,c_67]) ).
cnf(c_264,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_260,c_67]) ).
cnf(c_266,plain,
( product(A,e_3,e_2)
| ~ product(e_4,e_2,A)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_261,c_67]) ).
cnf(c_267,plain,
( product(e_3,A,e_4)
| ~ product(e_4,e_2,A)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_261,c_67]) ).
cnf(c_269,plain,
( ~ product(e_1,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_261,c_19]) ).
cnf(c_273,plain,
( ~ product(e_1,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_262,c_20]) ).
cnf(c_274,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_269,c_260]) ).
cnf(c_277,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_274,c_30]) ).
cnf(c_358,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_176,c_73]) ).
cnf(c_359,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_171,c_358]) ).
cnf(c_278,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_147,c_359]) ).
cnf(c_360,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_176,c_72]) ).
cnf(c_361,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_170,c_360]) ).
cnf(c_279,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_146,c_361]) ).
cnf(c_362,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_278,c_264]) ).
cnf(c_281,plain,
( product(e_1,e_4,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_157,c_362]) ).
cnf(c_363,plain,
( product(e_3,e_3,e_4)
| product(e_2,e_4,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_279,c_267]) ).
cnf(c_291,plain,
( product(e_2,e_4,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_157,c_363]) ).
cnf(c_364,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_281,c_263]) ).
cnf(c_302,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_365,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_291,c_266]) ).
cnf(c_311,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_365]) ).
cnf(c_366,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_302,c_277]) ).
cnf(c_328,plain,
product(e_1,e_4,e_2),
inference(copy,[status(thm)],[c_366]) ).
cnf(c_329,plain,
product(e_3,e_4,e_1),
inference(resolve,[status(thm)],[c_328,c_273]) ).
cnf(c_332,plain,
~ product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_328,c_30]) ).
cnf(c_336,plain,
product(e_2,e_4,e_1),
inference(resolve,[status(thm)],[c_332,c_311]) ).
cnf(c_367,plain,
~ product(e_2,e_4,e_1),
inference(resolve,[status(thm)],[c_329,c_21]) ).
cnf(c_351,plain,
$false,
inference(resolve,[status(thm)],[c_336,c_367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:21:48 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 2470224 was started by sandbox on n017,
% 0.17/0.44 % Fri Sep 25 14:21:48 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.52
% 0.17/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.52
% 0.17/0.52 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.17/0.52 % Length of proof is 61.
% 0.17/0.52 % Level of proof is 10.
% 0.17/0.52 % Maximum clause weight is 20.000.
% 0.17/0.52 % Given clauses 196.
% 0.17/0.52
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------