%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP128-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:27:52 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 50 ~; 64 |; 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 : 68 ( 3 sgn 26 !; 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_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(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]) ).
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_9,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_11,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_14,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_17,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_0,VAR_2,VAR_3)
| ~ product(VAR_2,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_19,plain,
( product(A,C,D)
| ~ product(C,B,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_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]) ).
fof(qg3_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_3,VAR_1,VAR_0)
| ~ product(VAR_3,VAR_0,VAR_2)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_2) ).
cnf(c_24,plain,
( ~ product(D,B,A)
| ~ product(D,A,C)
| 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_1,VAR_3)
| ~ product(VAR_0,VAR_2,VAR_3)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_1) ).
cnf(c_25,plain,
( ~ product(C,B,D)
| ~ product(A,C,D)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg3_1]) ).
cnf(c_28,plain,
( product(A,A,A)
| ~ product(A,B,A) ),
inference(factor,[status(thm)],[c_19]) ).
cnf(c_29,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_30,plain,
( ~ product(B,A,A)
| product(A,A,A) ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_31,plain,
( ~ product(A,A,B)
| product(A,A,A) ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_34,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_35,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_21,c_20]) ).
cnf(c_52,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_29,c_23]) ).
cnf(c_61,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_34,c_23]) ).
cnf(c_140,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_52,c_31]) ).
cnf(c_63,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_141,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_63,c_31]) ).
cnf(c_64,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_65,plain,
~ product(e_1,e_1,e_3),
inference(resolve,[status(thm)],[c_17,c_64]) ).
cnf(c_67,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_14,c_64]) ).
cnf(c_69,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_11,c_64]) ).
cnf(c_71,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_67,c_61]) ).
cnf(c_72,plain,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_71,c_30]) ).
cnf(c_142,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_35,c_23]) ).
cnf(c_81,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_69,c_142]) ).
cnf(c_87,plain,
( ~ product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_72,c_11]) ).
cnf(c_88,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_81,c_28]) ).
cnf(c_143,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_87,c_71]) ).
cnf(c_100,plain,
product(e_1,e_3,e_2),
inference(copy,[status(thm)],[c_143]) ).
cnf(c_144,plain,
( ~ product(e_3,e_1,A)
| ~ product(e_1,e_3,A) ),
inference(resolve,[status(thm)],[c_25,c_65]) ).
cnf(c_108,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_144,c_100]) ).
cnf(c_122,plain,
product(e_3,e_3,e_3),
inference(resolve,[status(thm)],[c_108,c_88]) ).
cnf(c_123,plain,
product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_108,c_81]) ).
cnf(c_145,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_122,c_14]) ).
cnf(c_139,plain,
$false,
inference(resolve,[status(thm)],[c_123,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP128-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n018.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 14:30:21 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 2163275 was started by sandbox2 on n018,
% 0.20/0.45 % Fri Sep 25 14:30:21 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.20/0.49
% 0.20/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.49
% 0.20/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.20/0.49 % Length of proof is 36.
% 0.20/0.49 % Level of proof is 12.
% 0.20/0.49 % Maximum clause weight is 16.000.
% 0.20/0.49 % Given clauses 50.
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------