%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:27:41 AM UTC 2026
% Result : Unsatisfiable 0.11s 10.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 40 unt; 0 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 81 ~; 110 |; 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 : 73 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_2,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_3,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_4,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_6,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_7,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_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_14,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_15,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_17,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_18,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_20,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_21,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_23,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_24,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_25,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_26,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_27,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_3,VAR_0,VAR_1)
| ~ product(VAR_2,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_34,plain,
( product(D,A,B)
| ~ product(C,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_35,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_36,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_37,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_38,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_39,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_40,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(qg3_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_1,VAR_3,VAR_0)
| ~ product(VAR_2,VAR_1,VAR_3)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_2) ).
cnf(c_41,plain,
( ~ product(B,D,A)
| ~ product(C,B,D)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg3_2]) ).
fof(qg3_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_2,VAR_0,VAR_3)
| ~ product(VAR_3,VAR_0,VAR_1)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_1) ).
cnf(c_42,plain,
( ~ product(C,A,D)
| ~ product(D,A,B)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg3_1]) ).
cnf(c_59,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_35,c_25]) ).
cnf(c_60,plain,
~ product(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_35,c_24]) ).
cnf(c_61,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_35,c_23]) ).
cnf(c_63,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_21]) ).
cnf(c_64,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_20]) ).
cnf(c_65,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_35,c_19]) ).
cnf(c_66,plain,
~ product(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_35,c_18]) ).
cnf(c_75,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_27,c_35]) ).
cnf(c_76,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_26,c_35]) ).
cnf(c_77,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_25,c_35]) ).
cnf(c_78,plain,
~ product(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_24,c_35]) ).
cnf(c_82,plain,
~ product(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_20,c_35]) ).
cnf(c_84,plain,
~ product(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_18,c_35]) ).
cnf(c_85,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_17,c_35]) ).
cnf(c_87,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_37,c_36]) ).
cnf(c_89,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_38,c_36]) ).
cnf(c_90,plain,
( product(e_3,A,e_4)
| 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_38,c_36]) ).
cnf(c_302,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_87,c_40]) ).
cnf(c_303,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_77,c_302]) ).
cnf(c_113,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_65,c_303]) ).
cnf(c_304,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_87,c_39]) ).
cnf(c_305,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_76,c_304]) ).
cnf(c_114,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_64,c_305]) ).
cnf(c_306,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_87,c_38]) ).
cnf(c_307,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_75,c_306]) ).
cnf(c_115,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_63,c_307]) ).
cnf(c_121,plain,
( product(A,e_1,e_4)
| ~ product(e_3,e_1,A)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_113,c_34]) ).
cnf(c_123,plain,
( ~ product(e_3,e_4,A)
| product(e_4,A,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_114,c_42]) ).
cnf(c_125,plain,
( ~ product(A,e_2,e_4)
| product(e_3,e_2,A)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_114,c_41]) ).
cnf(c_308,plain,
( product(e_3,e_4,e_1)
| product(e_4,e_2,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_123,c_115]) ).
cnf(c_158,plain,
( product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_82,c_308]) ).
cnf(c_166,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_158,c_26]) ).
cnf(c_309,plain,
( product(e_2,e_3,e_4)
| 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_89,c_39]) ).
cnf(c_310,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_78,c_309]) ).
cnf(c_202,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_66,c_310]) ).
cnf(c_311,plain,
( product(e_3,e_1,e_4)
| 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_90,c_40]) ).
cnf(c_312,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_85,c_311]) ).
cnf(c_212,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_61,c_312]) ).
cnf(c_313,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_90,c_39]) ).
cnf(c_314,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_84,c_313]) ).
cnf(c_213,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_60,c_314]) ).
cnf(c_227,plain,
( ~ product(e_2,e_1,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_202,c_23]) ).
cnf(c_315,plain,
( product(e_4,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_212,c_121]) ).
cnf(c_238,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_59,c_315]) ).
cnf(c_316,plain,
( product(e_3,e_2,e_3)
| product(e_2,e_4,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_213,c_125]) ).
cnf(c_246,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_60,c_316]) ).
cnf(c_317,plain,
( product(e_2,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_238,c_121]) ).
cnf(c_265,plain,
( product(e_2,e_1,e_4)
| product(e_1,e_4,e_2) ),
inference(copy,[status(thm)],[c_317]) ).
cnf(c_318,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_246,c_166]) ).
cnf(c_272,plain,
product(e_2,e_4,e_1),
inference(copy,[status(thm)],[c_318]) ).
cnf(c_279,plain,
~ product(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_272,c_27]) ).
cnf(c_319,plain,
( ~ product(e_2,e_4,A)
| ~ product(A,e_4,e_2) ),
inference(resolve,[status(thm)],[c_42,c_82]) ).
cnf(c_280,plain,
~ product(e_1,e_4,e_2),
inference(resolve,[status(thm)],[c_319,c_272]) ).
cnf(c_287,plain,
~ product(e_2,e_1,e_4),
inference(resolve,[status(thm)],[c_279,c_227]) ).
cnf(c_320,plain,
product(e_2,e_1,e_4),
inference(resolve,[status(thm)],[c_280,c_265]) ).
cnf(c_301,plain,
$false,
inference(resolve,[status(thm)],[c_287,c_320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/10.39 % Computer : n004.cluster.edu
% 0.07/10.39 % Model : x86_64 x86_64
% 0.07/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.39 % Memory : 8046.5625MB
% 0.07/10.39 % OS : Linux 6.8.0-71-generic
% 0.07/10.39 % CPULimit : 300
% 0.07/10.39 % WCLimit : 300
% 0.07/10.39 % DateTime : Fri Sep 25 14:27:17 UTC 2026
% 0.07/10.39 % CPUTime :
% 0.11/10.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.40 % Process 3373734 was started by sandbox on n004,
% 0.11/10.40 % Fri Sep 25 14:27:17 2026
% 0.11/10.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.40
% 0.11/10.40 % From the command line: assign(max_seconds, 300).
% 0.11/10.46
% 0.11/10.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/10.46
% 0.11/10.46 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/10.46 % Length of proof is 63.
% 0.11/10.46 % Level of proof is 10.
% 0.11/10.46 % Maximum clause weight is 20.000.
% 0.11/10.46 % Given clauses 134.
% 0.11/10.46
% 0.11/10.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------