%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP123-7.003 : 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 : 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 0.15s 0.38s
% Output : CNFRefutation 0.15s
% 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_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_9,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
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(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_18,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_24,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_2,A,B) ),
inference(resolve,[status(thm)],[c_18,c_12]) ).
cnf(c_25,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_2,B) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_35,plain,
( ~ product2(A,B,e_2)
| ~ product2(A,B,e_3) ),
inference(resolve,[status(thm)],[c_9,c_13]) ).
cnf(c_36,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_37,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_39,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_40,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_41,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_42,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_43,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_45,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_46,plain,
( product2(D,A,B)
| ~ product1(C,B,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[qg1a]) ).
cnf(c_50,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_42,c_41]) ).
cnf(c_52,plain,
( product1(e_1,A,e_3)
| product1(e_1,A,e_2)
| product1(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_42,c_39]) ).
cnf(c_57,plain,
~ product1(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_43,c_37]) ).
cnf(c_64,plain,
~ product1(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_43,c_24]) ).
cnf(c_67,plain,
~ product1(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_36,c_43]) ).
cnf(c_72,plain,
~ product1(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_25,c_43]) ).
cnf(c_80,plain,
~ product2(e_3,e_3,e_2),
inference(resolve,[status(thm)],[c_45,c_35]) ).
cnf(c_117,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_50,c_40]) ).
cnf(c_118,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_67,c_117]) ).
cnf(c_100,plain,
product1(e_3,e_2,e_1),
inference(resolve,[status(thm)],[c_57,c_118]) ).
cnf(c_103,plain,
( product2(A,e_3,e_2)
| ~ product1(e_1,e_2,A) ),
inference(resolve,[status(thm)],[c_100,c_46]) ).
cnf(c_119,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_52,c_40]) ).
cnf(c_120,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_2) ),
inference(resolve,[status(thm)],[c_72,c_119]) ).
cnf(c_113,plain,
product1(e_1,e_2,e_3),
inference(resolve,[status(thm)],[c_64,c_120]) ).
cnf(c_121,plain,
product2(e_3,e_3,e_2),
inference(resolve,[status(thm)],[c_113,c_103]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:29:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3515528 was started by sandbox on n001,
% 0.11/0.36 % Fri Sep 25 14:29:55 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 0.15/0.38
% 0.15/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.38
% 0.15/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.15/0.38 % Length of proof is 28.
% 0.15/0.38 % Level of proof is 5.
% 0.15/0.38 % Maximum clause weight is 16.000.
% 0.15/0.38 % Given clauses 54.
% 0.15/0.38
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------