%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:28:23 AM UTC 2026
% Result : Unsatisfiable 3.39s 0.95s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 122 ( 121 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 61 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 12 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_3,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_7,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_13,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != VAR_3
| multiply(VAR_4,VAR_3) != sk_c6
| inverse(VAR_2) != sk_c7
| multiply(VAR_2,sk_c7) != VAR_3
| multiply(sk_c7,VAR_1) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(E) != D
| multiply(E,D) != sk_c6
| inverse(C) != sk_c7
| multiply(C,sk_c7) != D
| multiply(sk_c7,B) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
cnf(c_1621,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1622,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1621]) ).
cnf(c_29,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1622]) ).
cnf(c_54,plain,
( inverse(C) != identity
| multiply(C,identity) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| multiply(sk_c7,B) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_1623,plain,
( inverse(B) != identity
| multiply(B,identity) != sk_c6
| multiply(sk_c7,A) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| multiply(inverse(sk_c7),sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_54]) ).
cnf(c_106,plain,
( inverse(B) != identity
| multiply(B,identity) != sk_c6
| multiply(sk_c7,A) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_1623]) ).
cnf(c_331,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_29]) ).
cnf(c_349,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_29,c_29]) ).
cnf(c_350,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_349,c_331]) ).
cnf(c_1624,plain,
( inverse(B) != identity
| B != sk_c6
| multiply(sk_c7,A) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_350,c_106]) ).
cnf(c_353,plain,
( inverse(B) != identity
| sk_c6 != B
| multiply(sk_c7,A) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_1624]) ).
cnf(c_360,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_350,c_2]) ).
cnf(c_441,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_349,c_2]) ).
cnf(c_459,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_349,c_29]) ).
cnf(c_1625,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_349,c_350]) ).
cnf(c_1626,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_350,c_1625]) ).
cnf(c_460,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_1626]) ).
cnf(c_1627,plain,
( inverse(B) != identity
| sk_c6 != B
| multiply(sk_c7,A) != sk_c6
| sk_c7 != sk_c7
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_460,c_353]) ).
cnf(c_467,plain,
( inverse(B) != identity
| sk_c6 != B
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_1627]) ).
cnf(c_533,plain,
( multiply(sk_c4,sk_c5) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_441]) ).
cnf(c_536,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_441]) ).
cnf(c_537,plain,
( multiply(sk_c4,sk_c5) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_441]) ).
cnf(c_1628,plain,
( sk_c6 != inverse(identity)
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6 ),
inference(resolve,[status(thm)],[c_467,c_460]) ).
cnf(c_1629,plain,
( sk_c6 != identity
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_360,c_1628]) ).
cnf(c_1630,plain,
( identity != sk_c6
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_1629]) ).
cnf(c_624,plain,
( multiply(sk_c7,A) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_1630]) ).
cnf(c_625,plain,
identity != sk_c6,
inference(resolve,[status(thm)],[c_624,c_459]) ).
cnf(c_793,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_537,c_441]) ).
cnf(c_1631,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_533,c_6]) ).
cnf(c_1632,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_1631]) ).
cnf(c_1480,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(resolve,[status(thm)],[c_625,c_1632]) ).
cnf(c_1633,plain,
( sk_c6 = identity
| multiply(sk_c4,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_1480,c_793]) ).
cnf(c_1634,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c5) = identity ),
inference(copy,[status(thm)],[c_1633]) ).
cnf(c_1605,plain,
multiply(sk_c4,sk_c5) = identity,
inference(resolve,[status(thm)],[c_625,c_1634]) ).
cnf(c_1635,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1605,c_536]) ).
cnf(c_1636,plain,
( sk_c6 = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1480,c_1635]) ).
cnf(c_1637,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1636]) ).
cnf(c_1638,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_1637]) ).
cnf(c_1620,plain,
$false,
inference(resolve,[status(thm)],[c_625,c_1638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n016.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 14:43:29 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2631915 was started by sandbox2 on n016,
% 0.19/0.45 % Fri Sep 25 14:43:29 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 3.39/0.95
% 3.39/0.95 % SZS status Unsatisfiable for theBenchmark
% 3.39/0.95
% 3.39/0.95 % Proof 1 at 0.36 (+ 0.12) seconds.
% 3.39/0.95 % Length of proof is 29.
% 3.39/0.95 % Level of proof is 10.
% 3.39/0.95 % Maximum clause weight is 32.000.
% 3.39/0.95 % Given clauses 127.
% 3.39/0.95
% 3.39/0.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------