%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-2.004 : 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 : n003.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 07:27:37 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 106 ( 46 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 244 ( 118 ~; 126 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 95 ( 0 sgn 26 !; 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_2_then_e_3,axiom,
next(e_2,e_3),
file('theBenchmark.p',e_2_then_e_3) ).
cnf(c_3,plain,
next(e_2,e_3),
inference(clausify,[status(thm)],[e_2_then_e_3]) ).
fof(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('theBenchmark.p',e_4_greater_e_3) ).
cnf(c_5,plain,
greater(e_4,e_3),
inference(clausify,[status(thm)],[e_4_greater_e_3]) ).
cnf(c_7,plain,
( ~ greater(A,e_3)
| ~ product(e_2,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
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(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_16,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_17,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_19,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_20,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_23,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_27,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_28,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
fof(qg2_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_5,VAR_3,VAR_4)
| ~ product(VAR_5,VAR_0,VAR_1)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2_1) ).
cnf(c_29,plain,
( equalish(A,D)
| ~ product(F,D,E)
| ~ product(F,A,B)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg2_1]) ).
fof(qg2_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_1,VAR_4)
| ~ product(VAR_5,VAR_3,VAR_4)
| ~ product(VAR_5,VAR_0,VAR_1)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2_2) ).
cnf(c_30,plain,
( equalish(B,E)
| ~ product(F,D,E)
| ~ product(F,A,B)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg2_2]) ).
cnf(c_33,plain,
( ~ product(D,C,e_2)
| ~ product(D,A,e_3)
| ~ product(C,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_34,plain,
( ~ product(D,C,e_1)
| ~ product(D,A,e_4)
| ~ product(C,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_30,c_17]) ).
cnf(c_41,plain,
( ~ product(D,e_2,C)
| ~ product(D,e_4,A)
| ~ product(e_2,C,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_29,c_16]) ).
cnf(c_43,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_44,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_46,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_28,c_17]) ).
cnf(c_47,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_28,c_16]) ).
cnf(c_48,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_49,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_50,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_27,c_20]) ).
cnf(c_52,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_27,c_17]) ).
cnf(c_53,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_27,c_16]) ).
cnf(c_54,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_27,c_15]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_61,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_62,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_63,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_64,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_65,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_66,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_67,plain,
~ product(e_2,e_1,e_4),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_487,plain,
( ~ product(e_2,e_4,A)
| ~ product(e_2,e_2,e_2)
| ~ product(e_4,A,e_2) ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_111,plain,
( ~ product(e_2,e_4,A)
| ~ product(e_4,A,e_2) ),
inference(resolve,[status(thm)],[c_61,c_487]) ).
cnf(c_125,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_61,c_52]) ).
cnf(c_128,plain,
~ product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_61,c_49]) ).
cnf(c_129,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_61,c_48]) ).
cnf(c_130,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_61,c_47]) ).
cnf(c_131,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_61,c_46]) ).
cnf(c_133,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_61,c_44]) ).
cnf(c_169,plain,
( ~ product(B,e_1,e_1)
| ~ product(B,A,e_4)
| ~ product(A,e_4,e_1) ),
inference(resolve,[status(thm)],[c_61,c_34]) ).
cnf(c_173,plain,
( ~ product(B,e_2,e_2)
| ~ product(B,A,e_3)
| ~ product(A,e_3,e_2) ),
inference(resolve,[status(thm)],[c_61,c_33]) ).
cnf(c_187,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_54,c_61]) ).
cnf(c_188,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_53,c_61]) ).
cnf(c_189,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_52,c_61]) ).
cnf(c_191,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_50,c_61]) ).
cnf(c_195,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_46,c_61]) ).
cnf(c_198,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_43,c_61]) ).
cnf(c_199,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_63,c_62]) ).
cnf(c_200,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_63,c_62]) ).
cnf(c_201,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_64,c_62]) ).
cnf(c_204,plain,
( product(e_2,A,e_4)
| 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_65,c_62]) ).
cnf(c_488,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_199,c_66]) ).
cnf(c_489,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_189,c_488]) ).
cnf(c_207,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_131,c_489]) ).
cnf(c_490,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_199,c_65]) ).
cnf(c_491,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_188,c_490]) ).
cnf(c_208,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_130,c_491]) ).
cnf(c_492,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_199,c_64]) ).
cnf(c_493,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_187,c_492]) ).
cnf(c_209,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_129,c_493]) ).
cnf(c_228,plain,
( ~ product(e_1,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_208,c_43]) ).
cnf(c_244,plain,
( ~ product(e_1,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_209,c_44]) ).
cnf(c_257,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_228,c_207]) ).
cnf(c_259,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_257,c_111]) ).
cnf(c_494,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_200,c_66]) ).
cnf(c_495,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_195,c_494]) ).
cnf(c_316,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_125,c_495]) ).
cnf(c_496,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_201,c_66]) ).
cnf(c_497,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_191,c_496]) ).
cnf(c_319,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_133,c_497]) ).
cnf(c_327,plain,
( ~ product(e_2,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_316,c_47]) ).
cnf(c_498,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_3,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_319,c_169]) ).
cnf(c_386,plain,
( ~ product(e_3,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_61,c_498]) ).
cnf(c_499,plain,
( product(e_2,e_1,e_4)
| 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_204,c_66]) ).
cnf(c_500,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_198,c_499]) ).
cnf(c_501,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_128,c_500]) ).
cnf(c_476,plain,
product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_67,c_501]) ).
cnf(c_477,plain,
product(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_476,c_327]) ).
cnf(c_480,plain,
product(e_1,e_4,e_2),
inference(resolve,[status(thm)],[c_477,c_259]) ).
cnf(c_482,plain,
product(e_3,e_4,e_1),
inference(resolve,[status(thm)],[c_480,c_244]) ).
cnf(c_483,plain,
product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_482,c_386]) ).
cnf(c_502,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_476,c_173]) ).
cnf(c_503,plain,
~ product(e_2,e_2,e_2),
inference(resolve,[status(thm)],[c_483,c_502]) ).
cnf(c_486,plain,
$false,
inference(resolve,[status(thm)],[c_61,c_503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:26:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 375148 was started by sandbox2 on n003,
% 0.10/0.37 % Fri Sep 25 14:26:22 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.42
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.42
% 0.10/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.42 % Length of proof is 70.
% 0.10/0.42 % Level of proof is 10.
% 0.10/0.42 % Maximum clause weight is 22.000.
% 0.10/0.42 % Given clauses 213.
% 0.10/0.42
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
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