%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP125-1.003 : 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 : 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 07:27:39 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 19 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 79 ( 39 ~; 40 |; 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 : 47 ( 0 sgn 19 !; 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(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_5,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_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_16,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_0)
| ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_19,plain,
( product(C,D,A)
| ~ product(B,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_20,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_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_21,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_22,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_24,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_31,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_20,c_16]) ).
cnf(c_33,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_20,c_14]) ).
cnf(c_36,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_42,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_14,c_20]) ).
cnf(c_45,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_11,c_20]) ).
cnf(c_47,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_22,c_21]) ).
cnf(c_48,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_22,c_21]) ).
cnf(c_62,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_47,c_24]) ).
cnf(c_63,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_42,c_62]) ).
cnf(c_53,plain,
product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_36,c_63]) ).
cnf(c_64,plain,
( product(e_2,A,e_1)
| ~ product(e_3,e_1,A) ),
inference(resolve,[status(thm)],[c_19,c_53]) ).
cnf(c_57,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_64,c_31]) ).
cnf(c_65,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_48,c_24]) ).
cnf(c_66,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_45,c_65]) ).
cnf(c_67,plain,
product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_57,c_66]) ).
cnf(c_61,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP125-1.003 : 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 : n018.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:27:50 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 2158833 was started by sandbox2 on n018,
% 0.10/0.37 % Fri Sep 25 14:27:50 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 23.
% 0.10/0.39 % Level of proof is 5.
% 0.10/0.39 % Maximum clause weight is 21.000.
% 0.10/0.39 % Given clauses 39.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------