%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 23 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 84 ( 42 ~; 42 |; 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 : 53 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_6,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_8,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_11,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_12,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_13,plain,
( equalish(C,D)
| ~ product2(A,B,D)
| ~ product2(A,B,C) ),
inference(clausify,[status(thm)],[product2_total_function2]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_28,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_29,plain,
group_element(e_2),
inference(clausify,[status(thm)],[element_2]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_30,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
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_31,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(product1_idempotence,axiom,
! [VAR_0] : product1(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product1_idempotence) ).
cnf(c_32,plain,
product1(A,A,A),
inference(clausify,[status(thm)],[product1_idempotence]) ).
fof(product2_idempotence,axiom,
! [VAR_0] : product2(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product2_idempotence) ).
cnf(c_34,plain,
product2(A,A,A),
inference(clausify,[status(thm)],[product2_idempotence]) ).
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_35,plain,
( product2(D,A,B)
| ~ product1(C,B,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[qg1a]) ).
cnf(c_55,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_56,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_2,B) ),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_58,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_59,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_2,A,B) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_61,plain,
( ~ product2(A,B,e_1)
| ~ product2(A,B,e_3) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_107,plain,
( product1(e_3,A,e_3)
| product1(e_3,A,e_2)
| product1(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
cnf(c_108,plain,
( product1(e_2,A,e_3)
| product1(e_2,A,e_2)
| product1(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_31,c_29]) ).
cnf(c_154,plain,
~ product1(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_55,c_32]) ).
cnf(c_156,plain,
~ product1(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_56,c_32]) ).
cnf(c_161,plain,
~ product1(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_163,plain,
~ product1(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_59,c_32]) ).
cnf(c_166,plain,
~ product2(e_3,e_3,e_1),
inference(resolve,[status(thm)],[c_61,c_34]) ).
cnf(c_217,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_107,c_28]) ).
cnf(c_218,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_161,c_217]) ).
cnf(c_199,plain,
product1(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_154,c_218]) ).
cnf(c_210,plain,
( product2(A,e_3,e_1)
| ~ product1(e_2,e_1,A) ),
inference(resolve,[status(thm)],[c_199,c_35]) ).
cnf(c_219,plain,
( product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_108,c_28]) ).
cnf(c_220,plain,
( product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_163,c_219]) ).
cnf(c_212,plain,
product1(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_156,c_220]) ).
cnf(c_221,plain,
product2(e_3,e_3,e_1),
inference(resolve,[status(thm)],[c_212,c_210]) ).
cnf(c_216,plain,
$false,
inference(resolve,[status(thm)],[c_166,c_221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 14:24:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 421778 was started by sandbox on n014,
% 0.10/0.36 % Fri Sep 25 14:24:02 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.38 % Length of proof is 28.
% 0.14/0.38 % Level of proof is 5.
% 0.14/0.38 % Maximum clause weight is 16.000.
% 0.14/0.38 % Given clauses 112.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------