%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP135-2.002 : 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 : n007.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 07:28:06 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 33 ~; 42 |; 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn 14 !; 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(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_10,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_11,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_3,VAR_0,VAR_1)
| ~ product(VAR_2,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_13,plain,
( product(D,A,B)
| ~ product(C,A,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_2)
| product(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product_total_function1) ).
cnf(c_14,plain,
( 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_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_15,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_16,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_17,plain,
( product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_14]) ).
cnf(c_18,plain,
( product(A,e_2,e_2)
| product(A,e_2,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_19,plain,
( product(e_2,A,e_2)
| product(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_22,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_23,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_24,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_26,plain,
( product(A,e_1,e_1)
| ~ product(e_2,e_1,A)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_27,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_31,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_23,c_10]) ).
cnf(c_35,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_19,c_16]) ).
cnf(c_36,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_31,c_24]) ).
cnf(c_41,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_35,c_10]) ).
cnf(c_42,plain,
( product(e_1,e_2,A)
| ~ product(e_2,A,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_36,c_13]) ).
cnf(c_45,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_51,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_41,c_22]) ).
cnf(c_52,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_45,c_35]) ).
cnf(c_60,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_51,c_27]) ).
cnf(c_53,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_57,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_11,c_53]) ).
cnf(c_58,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_10,c_53]) ).
cnf(c_61,plain,
product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_57,c_52]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_58,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:28:53 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1206807 was started by sandbox2 on n007,
% 0.19/0.45 % Fri Sep 25 14:28:53 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.47
% 0.19/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.47 % Length of proof is 29.
% 0.19/0.47 % Level of proof is 8.
% 0.19/0.47 % Maximum clause weight is 12.000.
% 0.19/0.47 % Given clauses 30.
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------