%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP123-6.003 : 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 : n001.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 07:27:36 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 23 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 81 ( 42 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_2,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_3,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_is_not_e_1]) ).
fof(product1_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product1(VAR_0,VAR_3,VAR_2)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_right_cancellation) ).
cnf(c_8,plain,
( equalish(B,D)
| ~ product1(A,D,C)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_right_cancellation]) ).
fof(product1_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product1(VAR_3,VAR_1,VAR_2)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_left_cancellation) ).
cnf(c_9,plain,
( equalish(A,D)
| ~ product1(D,B,C)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_left_cancellation]) ).
fof(product2_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product2(VAR_0,VAR_1,VAR_3)
| ~ product2(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product2_total_function2) ).
cnf(c_10,plain,
( equalish(C,D)
| ~ product2(A,B,D)
| ~ product2(A,B,C) ),
inference(clausify,[status(thm)],[product2_total_function2]) ).
cnf(c_21,plain,
( ~ product2(A,B,e_2)
| ~ product2(A,B,e_3) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_23,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_24,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_26,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_27,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
fof(qg1a,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product2(VAR_3,VAR_0,VAR_1)
| ~ product1(VAR_2,VAR_1,VAR_3)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg1a) ).
cnf(c_31,plain,
( product2(D,A,B)
| ~ product1(C,B,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[qg1a]) ).
fof(product2_idempotence,axiom,
! [VAR_0] : product2(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product2_idempotence) ).
cnf(c_32,plain,
product2(A,A,A),
inference(clausify,[status(thm)],[product2_idempotence]) ).
fof(product1_idempotence,axiom,
! [VAR_0] : product1(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product1_idempotence) ).
cnf(c_34,plain,
product1(A,A,A),
inference(clausify,[status(thm)],[product1_idempotence]) ).
fof(product1_total_function1,axiom,
! [VAR_0,VAR_1] :
( product1(VAR_0,VAR_1,e_3)
| product1(VAR_0,VAR_1,e_2)
| product1(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product1_total_function1) ).
cnf(c_35,plain,
( product1(A,B,e_3)
| product1(A,B,e_2)
| product1(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product1_total_function1]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_36,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_37,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_38,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_42,plain,
~ product2(e_2,e_2,e_3),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_68,plain,
~ product1(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_34,c_27]) ).
cnf(c_70,plain,
~ product1(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_34,c_26]) ).
cnf(c_75,plain,
~ product1(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_34,c_24]) ).
cnf(c_77,plain,
~ product1(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_34,c_23]) ).
cnf(c_80,plain,
( product1(A,e_3,e_3)
| product1(A,e_3,e_2)
| product1(A,e_3,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_97,plain,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_80,c_38]) ).
cnf(c_98,plain,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_70,c_97]) ).
cnf(c_92,plain,
product1(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_77,c_98]) ).
cnf(c_99,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_80,c_37]) ).
cnf(c_100,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_68,c_99]) ).
cnf(c_93,plain,
product1(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_75,c_100]) ).
cnf(c_101,plain,
( product2(e_2,A,e_3)
| ~ product1(A,e_3,e_1) ),
inference(resolve,[status(thm)],[c_31,c_92]) ).
cnf(c_102,plain,
~ product1(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_101,c_42]) ).
cnf(c_96,plain,
$false,
inference(resolve,[status(thm)],[c_93,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:29:10 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3513988 was started by sandbox2 on n001,
% 0.16/0.44 % Fri Sep 25 14:29:10 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 26.
% 0.16/0.46 % Level of proof is 4.
% 0.16/0.46 % Maximum clause weight is 18.000.
% 0.16/0.46 % Given clauses 39.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------