%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:31:24 AM UTC 2026
% Result : Unsatisfiable 8.99s 2.91s
% Output : CNFRefutation 8.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 87 unt; 0 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos01,axiom,
! [VAR_0] : product(VAR_0,one) = VAR_0,
file('theBenchmark.p',sos01) ).
cnf(c_1,plain,
product(A,one) = A,
inference(clausify,[status(thm)],[sos01]) ).
fof(sos02,axiom,
! [VAR_0] : product(one,VAR_0) = VAR_0,
file('theBenchmark.p',sos02) ).
cnf(c_2,plain,
product(one,A) = A,
inference(clausify,[status(thm)],[sos02]) ).
fof(sos03,axiom,
! [VAR_0,VAR_1] : product(VAR_0,difference(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',sos03) ).
cnf(c_3,plain,
product(A,difference(A,B)) = B,
inference(clausify,[status(thm)],[sos03]) ).
fof(sos05,axiom,
! [VAR_0,VAR_1] : quotient(product(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',sos05) ).
cnf(c_5,plain,
quotient(product(A,B),B) = A,
inference(clausify,[status(thm)],[sos05]) ).
fof(sos06,axiom,
! [VAR_0,VAR_1] : product(quotient(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',sos06) ).
cnf(c_6,plain,
product(quotient(A,B),B) = A,
inference(clausify,[status(thm)],[sos06]) ).
fof(sos07,axiom,
! [VAR_0,VAR_1,VAR_2] : difference(VAR_0,product(product(VAR_0,VAR_1),VAR_2)) = quotient(product(VAR_1,product(VAR_2,VAR_0)),VAR_0),
file('theBenchmark.p',sos07) ).
cnf(c_7,plain,
difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A),
inference(clausify,[status(thm)],[sos07]) ).
fof(sos09,axiom,
! [VAR_0] : i(VAR_0) = difference(VAR_0,one),
file('theBenchmark.p',sos09) ).
cnf(c_9,plain,
i(A) = difference(A,one),
inference(clausify,[status(thm)],[sos09]) ).
fof(sos10,axiom,
! [VAR_0] : j(VAR_0) = quotient(one,VAR_0),
file('theBenchmark.p',sos10) ).
cnf(c_10,plain,
j(A) = quotient(one,A),
inference(clausify,[status(thm)],[sos10]) ).
fof(sos11,axiom,
! [VAR_0] : product(i(VAR_0),VAR_0) = product(VAR_0,j(VAR_0)),
file('theBenchmark.p',sos11) ).
cnf(c_11,plain,
product(i(A),A) = product(A,j(A)),
inference(clausify,[status(thm)],[sos11]) ).
cnf(c_3464,plain,
product(difference(A,one),A) = product(A,j(A)),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_12,plain,
product(difference(A,one),A) = product(A,quotient(one,A)),
inference(paramod,[status(thm)],[c_10,c_3464]) ).
fof(sos12,axiom,
! [VAR_0] : eta(VAR_0) = product(i(VAR_0),VAR_0),
file('theBenchmark.p',sos12) ).
cnf(c_13,plain,
eta(A) = product(i(A),A),
inference(clausify,[status(thm)],[sos12]) ).
cnf(c_3465,plain,
eta(A) = product(difference(A,one),A),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_14,plain,
eta(A) = product(A,quotient(one,A)),
inference(paramod,[status(thm)],[c_12,c_3465]) ).
fof(sos14,axiom,
! [VAR_0,VAR_1] : product(VAR_0,product(eta(VAR_0),VAR_1)) = product(j(j(VAR_0)),VAR_1),
file('theBenchmark.p',sos14) ).
cnf(c_17,plain,
product(A,product(eta(A),B)) = product(j(j(A)),B),
inference(clausify,[status(thm)],[sos14]) ).
cnf(c_3466,plain,
product(A,product(product(A,quotient(one,A)),B)) = product(j(j(A)),B),
inference(paramod,[status(thm)],[c_14,c_17]) ).
cnf(c_3467,plain,
product(A,product(product(A,quotient(one,A)),B)) = product(j(quotient(one,A)),B),
inference(paramod,[status(thm)],[c_10,c_3466]) ).
cnf(c_3468,plain,
product(A,product(product(A,quotient(one,A)),B)) = product(quotient(one,quotient(one,A)),B),
inference(paramod,[status(thm)],[c_10,c_3467]) ).
cnf(c_18,plain,
product(quotient(one,quotient(one,A)),B) = product(A,product(product(A,quotient(one,A)),B)),
inference(copy,[status(thm)],[c_3468]) ).
fof(sos16,axiom,
! [VAR_0,VAR_1,VAR_2] : product(eta(VAR_0),product(VAR_1,VAR_2)) = product(product(eta(VAR_0),VAR_1),VAR_2),
file('theBenchmark.p',sos16) ).
cnf(c_21,plain,
product(eta(A),product(B,C)) = product(product(eta(A),B),C),
inference(clausify,[status(thm)],[sos16]) ).
cnf(c_3469,plain,
product(product(A,quotient(one,A)),product(B,C)) = product(product(eta(A),B),C),
inference(paramod,[status(thm)],[c_14,c_21]) ).
cnf(c_3470,plain,
product(product(A,quotient(one,A)),product(B,C)) = product(product(product(A,quotient(one,A)),B),C),
inference(paramod,[status(thm)],[c_14,c_3469]) ).
cnf(c_22,plain,
product(product(product(A,quotient(one,A)),B),C) = product(product(A,quotient(one,A)),product(B,C)),
inference(copy,[status(thm)],[c_3470]) ).
fof(goals,axiom,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('theBenchmark.p',goals) ).
cnf(c_30,plain,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_3471,plain,
product(j(quotient(one,x0)),j(product(x1,x0))) != j(x1),
inference(paramod,[status(thm)],[c_10,c_30]) ).
cnf(c_3472,plain,
product(quotient(one,quotient(one,x0)),j(product(x1,x0))) != j(x1),
inference(paramod,[status(thm)],[c_10,c_3471]) ).
cnf(c_3473,plain,
product(quotient(one,quotient(one,x0)),quotient(one,product(x1,x0))) != j(x1),
inference(paramod,[status(thm)],[c_10,c_3472]) ).
cnf(c_3474,plain,
product(x0,product(product(x0,quotient(one,x0)),quotient(one,product(x1,x0)))) != j(x1),
inference(paramod,[status(thm)],[c_18,c_3473]) ).
cnf(c_31,plain,
product(x0,product(product(x0,quotient(one,x0)),quotient(one,product(x1,x0)))) != quotient(one,x1),
inference(paramod,[status(thm)],[c_10,c_3474]) ).
cnf(c_38,plain,
product(A,quotient(product(B,product(C,A)),A)) = product(product(A,B),C),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_49,plain,
product(A,product(product(A,quotient(one,A)),quotient(one,A))) = one,
inference(paramod,[status(thm)],[c_18,c_6]) ).
cnf(c_61,plain,
quotient(product(product(A,quotient(one,A)),product(B,C)),C) = product(product(A,quotient(one,A)),B),
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_98,plain,
quotient(product(product(A,B),C),quotient(product(B,product(C,A)),A)) = A,
inference(paramod,[status(thm)],[c_38,c_5]) ).
cnf(c_99,plain,
product(A,quotient(product(B,C),A)) = product(product(A,B),quotient(C,A)),
inference(paramod,[status(thm)],[c_6,c_38]) ).
cnf(c_3475,plain,
product(A,quotient(B,A)) = product(product(A,quotient(B,product(C,A))),C),
inference(paramod,[status(thm)],[c_6,c_38]) ).
cnf(c_100,plain,
product(product(A,quotient(B,product(C,A))),C) = product(A,quotient(B,A)),
inference(copy,[status(thm)],[c_3475]) ).
cnf(c_138,plain,
quotient(one,product(product(A,quotient(one,A)),quotient(one,A))) = A,
inference(paramod,[status(thm)],[c_49,c_5]) ).
cnf(c_3476,plain,
quotient(one,product(product(product(product(A,quotient(one,A)),quotient(one,A)),A),quotient(one,product(product(A,quotient(one,A)),quotient(one,A))))) = product(product(A,quotient(one,A)),quotient(one,A)),
inference(paramod,[status(thm)],[c_138,c_138]) ).
cnf(c_3477,plain,
quotient(one,product(product(product(A,quotient(one,A)),product(quotient(one,A),A)),quotient(one,product(product(A,quotient(one,A)),quotient(one,A))))) = product(product(A,quotient(one,A)),quotient(one,A)),
inference(paramod,[status(thm)],[c_22,c_3476]) ).
cnf(c_3478,plain,
quotient(one,product(product(product(A,quotient(one,A)),one),quotient(one,product(product(A,quotient(one,A)),quotient(one,A))))) = product(product(A,quotient(one,A)),quotient(one,A)),
inference(paramod,[status(thm)],[c_6,c_3477]) ).
cnf(c_3479,plain,
quotient(one,product(product(A,quotient(one,A)),quotient(one,product(product(A,quotient(one,A)),quotient(one,A))))) = product(product(A,quotient(one,A)),quotient(one,A)),
inference(paramod,[status(thm)],[c_1,c_3478]) ).
cnf(c_189,plain,
quotient(one,product(product(A,quotient(one,A)),A)) = product(product(A,quotient(one,A)),quotient(one,A)),
inference(paramod,[status(thm)],[c_138,c_3479]) ).
cnf(c_3480,plain,
product(A,quotient(B,A)) = product(product(A,B),quotient(one,A)),
inference(paramod,[status(thm)],[c_1,c_99]) ).
cnf(c_234,plain,
product(product(A,B),quotient(one,A)) = product(A,quotient(B,A)),
inference(copy,[status(thm)],[c_3480]) ).
cnf(c_264,plain,
quotient(product(A,quotient(B,A)),quotient(one,A)) = product(A,B),
inference(paramod,[status(thm)],[c_234,c_5]) ).
cnf(c_329,plain,
quotient(product(A,B),quotient(one,A)) = product(A,product(B,A)),
inference(paramod,[status(thm)],[c_5,c_264]) ).
cnf(c_3481,plain,
quotient(product(product(quotient(one,A),A),B),product(A,product(product(B,quotient(one,A)),A))) = quotient(one,A),
inference(paramod,[status(thm)],[c_329,c_98]) ).
cnf(c_3482,plain,
quotient(product(one,B),product(A,product(product(B,quotient(one,A)),A))) = quotient(one,A),
inference(paramod,[status(thm)],[c_6,c_3481]) ).
cnf(c_406,plain,
quotient(A,product(B,product(product(A,quotient(one,B)),B))) = quotient(one,B),
inference(paramod,[status(thm)],[c_2,c_3482]) ).
cnf(c_530,plain,
quotient(product(A,quotient(B,A)),C) = product(A,quotient(B,product(C,A))),
inference(paramod,[status(thm)],[c_100,c_5]) ).
cnf(c_3483,plain,
product(A,product(product(B,quotient(one,B)),C)) = product(product(A,product(B,quotient(one,B))),quotient(product(C,A),A)),
inference(paramod,[status(thm)],[c_61,c_99]) ).
cnf(c_3484,plain,
product(A,product(product(B,quotient(one,B)),C)) = product(product(A,product(B,quotient(one,B))),C),
inference(paramod,[status(thm)],[c_5,c_3483]) ).
cnf(c_721,plain,
product(product(A,product(B,quotient(one,B))),C) = product(A,product(product(B,quotient(one,B)),C)),
inference(copy,[status(thm)],[c_3484]) ).
cnf(c_3485,plain,
quotient(product(A,quotient(one,A)),product(B,product(product(A,quotient(one,A)),product(quotient(one,B),B)))) = quotient(one,B),
inference(paramod,[status(thm)],[c_22,c_406]) ).
cnf(c_3486,plain,
quotient(product(A,quotient(one,A)),product(B,product(product(A,quotient(one,A)),one))) = quotient(one,B),
inference(paramod,[status(thm)],[c_6,c_3485]) ).
cnf(c_3487,plain,
quotient(product(A,quotient(one,A)),product(B,product(A,quotient(one,A)))) = quotient(one,B),
inference(paramod,[status(thm)],[c_1,c_3486]) ).
cnf(c_3488,plain,
product(A,quotient(one,product(product(B,product(A,quotient(one,A))),A))) = quotient(one,B),
inference(paramod,[status(thm)],[c_530,c_3487]) ).
cnf(c_1479,plain,
product(A,quotient(one,product(B,product(product(A,quotient(one,A)),A)))) = quotient(one,B),
inference(paramod,[status(thm)],[c_721,c_3488]) ).
cnf(c_1761,plain,
quotient(product(A,B),C) = product(A,quotient(product(B,A),product(C,A))),
inference(paramod,[status(thm)],[c_5,c_530]) ).
cnf(c_3489,plain,
quotient(product(product(product(A,quotient(one,A)),A),product(product(A,quotient(one,A)),quotient(one,A))),B) = product(product(product(A,quotient(one,A)),A),quotient(one,product(B,product(product(A,quotient(one,A)),A)))),
inference(paramod,[status(thm)],[c_189,c_530]) ).
cnf(c_3490,plain,
quotient(product(product(A,quotient(one,A)),product(A,product(product(A,quotient(one,A)),quotient(one,A)))),B) = product(product(product(A,quotient(one,A)),A),quotient(one,product(B,product(product(A,quotient(one,A)),A)))),
inference(paramod,[status(thm)],[c_22,c_3489]) ).
cnf(c_3491,plain,
quotient(product(product(A,quotient(one,A)),one),B) = product(product(product(A,quotient(one,A)),A),quotient(one,product(B,product(product(A,quotient(one,A)),A)))),
inference(paramod,[status(thm)],[c_49,c_3490]) ).
cnf(c_3492,plain,
quotient(product(A,quotient(one,A)),B) = product(product(product(A,quotient(one,A)),A),quotient(one,product(B,product(product(A,quotient(one,A)),A)))),
inference(paramod,[status(thm)],[c_1,c_3491]) ).
cnf(c_3493,plain,
product(A,quotient(one,product(B,A))) = product(product(product(A,quotient(one,A)),A),quotient(one,product(B,product(product(A,quotient(one,A)),A)))),
inference(paramod,[status(thm)],[c_530,c_3492]) ).
cnf(c_3494,plain,
product(A,quotient(one,product(B,A))) = product(product(A,quotient(one,A)),product(A,quotient(one,product(B,product(product(A,quotient(one,A)),A))))),
inference(paramod,[status(thm)],[c_22,c_3493]) ).
cnf(c_2359,plain,
product(A,quotient(one,product(B,A))) = product(product(A,quotient(one,A)),quotient(one,B)),
inference(paramod,[status(thm)],[c_1479,c_3494]) ).
cnf(c_3495,plain,
quotient(one,A) = product(B,quotient(product(product(product(B,quotient(one,B)),quotient(one,B)),B),product(A,B))),
inference(paramod,[status(thm)],[c_49,c_1761]) ).
cnf(c_3496,plain,
quotient(one,A) = product(B,quotient(product(product(B,quotient(one,B)),product(quotient(one,B),B)),product(A,B))),
inference(paramod,[status(thm)],[c_22,c_3495]) ).
cnf(c_3497,plain,
quotient(one,A) = product(B,quotient(product(product(B,quotient(one,B)),one),product(A,B))),
inference(paramod,[status(thm)],[c_6,c_3496]) ).
cnf(c_3498,plain,
quotient(one,A) = product(B,quotient(product(B,quotient(one,B)),product(A,B))),
inference(paramod,[status(thm)],[c_1,c_3497]) ).
cnf(c_3499,plain,
quotient(one,A) = product(B,product(B,quotient(one,product(product(A,B),B)))),
inference(paramod,[status(thm)],[c_530,c_3498]) ).
cnf(c_3500,plain,
quotient(one,A) = product(B,product(product(B,quotient(one,B)),quotient(one,product(A,B)))),
inference(paramod,[status(thm)],[c_2359,c_3499]) ).
cnf(c_3462,plain,
product(A,product(product(A,quotient(one,A)),quotient(one,product(B,A)))) = quotient(one,B),
inference(copy,[status(thm)],[c_3500]) ).
cnf(c_3463,plain,
$false,
inference(resolve,[status(thm)],[c_3462,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:48:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1750806 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 15:48:42 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 8.99/2.91
% 8.99/2.91 % SZS status Unsatisfiable for theBenchmark
% 8.99/2.91
% 8.99/2.91 % Proof 1 at 1.13 (+ 0.15) seconds.
% 8.99/2.91 % Length of proof is 37.
% 8.99/2.91 % Level of proof is 10.
% 8.99/2.91 % Maximum clause weight is 19.000.
% 8.99/2.91 % Given clauses 143.
% 8.99/2.91
% 8.99/2.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------