TSTP Solution File: GRP778+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRP778+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:29:58 EDT 2023
% Result : Theorem 28.07s 4.36s
% Output : Refutation 28.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 15
% Syntax : Number of formulae : 350 ( 340 unt; 0 def)
% Number of atoms : 360 ( 335 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 4 |; 0 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 330 (; 330 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73569,plain,
$false,
inference(subsumption_resolution,[],[f73568,f64658]) ).
fof(f64658,plain,
product(b1,b2) != product(b,quotient(b,b1)),
inference(forward_demodulation,[],[f64657,f62875]) ).
fof(f62875,plain,
product(difference(b2,b),b) = product(b,quotient(b,b1)),
inference(forward_demodulation,[],[f62874,f61583]) ).
fof(f61583,plain,
product(b1,quotient(b,b1)) = difference(b2,b),
inference(forward_demodulation,[],[f61543,f4346]) ).
fof(f4346,plain,
! [X1] : product(b1,quotient(X1,b1)) = quotient(product(a2,X1),c1),
inference(superposition,[],[f2550,f38]) ).
fof(f38,plain,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos04) ).
fof(f2550,plain,
! [X1] : product(b1,X1) = quotient(product(a2,product(X1,b1)),c1),
inference(superposition,[],[f36,f1032]) ).
fof(f1032,plain,
! [X39] : product(a2,product(X39,b1)) = product(product(b1,X39),c1),
inference(forward_demodulation,[],[f1031,f742]) ).
fof(f742,plain,
! [X2,X0,X1] : product(product(X1,X0),product(X2,X0)) = product(product(X1,X2),X0),
inference(superposition,[],[f42,f34]) ).
fof(f34,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] : product(X0,X0) = X0,
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1] : product(X1,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos06) ).
fof(f42,plain,
! [X2,X3,X0,X1] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : product(product(X1,X0),product(X3,X2)) = product(product(X1,X3),product(X0,X2)),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos05) ).
fof(f1031,plain,
! [X39] : product(a2,product(X39,b1)) = product(product(b1,c1),product(X39,c1)),
inference(forward_demodulation,[],[f894,f740]) ).
fof(f740,plain,
! [X56,X55] : product(product(a2,X55),product(b1,X56)) = product(product(b1,c1),product(X55,X56)),
inference(superposition,[],[f42,f55]) ).
fof(f55,plain,
product(a2,b1) = product(b1,c1),
inference(resolution,[],[f41,f28]) ).
fof(f28,plain,
d(a2,b1,c1),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
d(a2,b1,c1),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos13) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ d(X0,X1,X2)
| product(X0,X1) = product(X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( product(X0,X1) = product(X1,X2)
| ~ d(X0,X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( d(X0,X1,X2)
=> product(X0,X1) = product(X1,X2) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( d(X0,X1,X2)
<=> product(X0,X1) = product(X1,X2) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X4,X5,X6] :
( d(X4,X5,X6)
<=> product(X4,X5) = product(X5,X6) ),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos08) ).
fof(f894,plain,
! [X39] : product(a2,product(X39,b1)) = product(product(a2,X39),product(b1,c1)),
inference(superposition,[],[f720,f55]) ).
fof(f720,plain,
! [X2,X0,X1] : product(product(X0,X1),product(X0,X2)) = product(X0,product(X1,X2)),
inference(superposition,[],[f42,f34]) ).
fof(f36,plain,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos03) ).
fof(f61543,plain,
difference(b2,b) = quotient(product(a2,b),c1),
inference(superposition,[],[f36,f59109]) ).
fof(f59109,plain,
product(a2,b) = product(difference(b2,b),c1),
inference(forward_demodulation,[],[f59104,f45700]) ).
fof(f45700,plain,
! [X0] : product(difference(X0,b),c1) = product(b,product(a,quotient(X0,a))),
inference(forward_demodulation,[],[f45699,f35304]) ).
fof(f35304,plain,
! [X3,X4] : product(difference(X4,X3),X4) = product(X3,quotient(X4,X3)),
inference(backward_demodulation,[],[f34833,f35145]) ).
fof(f35145,plain,
! [X14,X15] : product(X14,quotient(X15,X14)) = difference(X14,product(difference(X15,X14),X14)),
inference(backward_demodulation,[],[f22440,f35139]) ).
fof(f35139,plain,
! [X3,X4] : difference(product(X4,X3),X3) = product(difference(X4,X3),X3),
inference(backward_demodulation,[],[f34233,f35138]) ).
fof(f35138,plain,
! [X2,X1] : difference(X2,X1) = difference(product(X1,quotient(X2,X1)),difference(product(X2,X1),X1)),
inference(forward_demodulation,[],[f35137,f38]) ).
fof(f35137,plain,
! [X2,X1] : difference(product(X1,quotient(X2,X1)),difference(product(X2,X1),X1)) = difference(product(quotient(X2,X1),X1),X1),
inference(forward_demodulation,[],[f35136,f148]) ).
fof(f148,plain,
! [X6,X7] : product(X7,product(X7,quotient(X6,X7))) = difference(product(X6,X7),X7),
inference(superposition,[],[f35,f90]) ).
fof(f90,plain,
! [X6,X5] : product(product(X5,X6),product(X6,product(X6,quotient(X5,X6)))) = X6,
inference(superposition,[],[f39,f38]) ).
fof(f39,plain,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos07) ).
fof(f35,plain,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos01) ).
fof(f35136,plain,
! [X2,X1] : difference(product(X1,quotient(X2,X1)),difference(product(X2,X1),X1)) = product(X1,product(X1,quotient(quotient(X2,X1),X1))),
inference(forward_demodulation,[],[f34880,f3520]) ).
fof(f3520,plain,
! [X29,X30] : product(X30,quotient(X29,X30)) = quotient(product(X30,X29),X30),
inference(superposition,[],[f1129,f38]) ).
fof(f1129,plain,
! [X10,X11] : product(X10,X11) = quotient(product(X10,product(X11,X10)),X10),
inference(superposition,[],[f36,f873]) ).
fof(f873,plain,
! [X0,X1] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[],[f720,f34]) ).
fof(f34880,plain,
! [X2,X1] : product(X1,quotient(product(X1,quotient(X2,X1)),X1)) = difference(product(X1,quotient(X2,X1)),difference(product(X2,X1),X1)),
inference(superposition,[],[f12289,f148]) ).
fof(f12289,plain,
! [X8,X7] : product(X7,quotient(X8,X7)) = difference(X8,product(X7,X8)),
inference(forward_demodulation,[],[f12235,f3520]) ).
fof(f12235,plain,
! [X8,X7] : difference(X8,product(X7,X8)) = quotient(product(X7,X8),X7),
inference(superposition,[],[f10816,f36]) ).
fof(f10816,plain,
! [X3,X4] : difference(X3,X4) = quotient(X4,quotient(X4,X3)),
inference(superposition,[],[f35,f10482]) ).
fof(f10482,plain,
! [X4,X5] : product(X5,quotient(X4,quotient(X4,X5))) = X4,
inference(forward_demodulation,[],[f10324,f4903]) ).
fof(f4903,plain,
! [X31,X28,X29,X30] : product(X28,quotient(X29,X30)) = quotient(product(product(X28,X31),X29),product(X31,X30)),
inference(superposition,[],[f36,f753]) ).
fof(f753,plain,
! [X38,X36,X37,X35] : product(product(X37,quotient(X35,X36)),product(X38,X36)) = product(product(X37,X38),X35),
inference(superposition,[],[f42,f38]) ).
fof(f10324,plain,
! [X4,X5] : quotient(product(product(X5,X4),X4),product(X4,quotient(X4,X5))) = X4,
inference(superposition,[],[f36,f9131]) ).
fof(f9131,plain,
! [X0,X1] : product(product(X0,X1),X1) = product(X1,product(X1,quotient(X1,X0))),
inference(forward_demodulation,[],[f9043,f8845]) ).
fof(f8845,plain,
! [X6,X5] : quotient(X5,product(X5,X6)) = product(X5,quotient(X5,X6)),
inference(superposition,[],[f8748,f48]) ).
fof(f48,plain,
! [X2,X3] : difference(quotient(X2,X3),X2) = X3,
inference(superposition,[],[f35,f38]) ).
fof(f8748,plain,
! [X28,X29] : product(X28,X29) = quotient(X28,product(X28,difference(X29,X28))),
inference(forward_demodulation,[],[f8747,f8727]) ).
fof(f8727,plain,
! [X0,X1] : product(product(product(difference(X1,difference(X1,product(X0,difference(X1,X0)))),X1),X0),X0) = X1,
inference(forward_demodulation,[],[f8381,f46]) ).
fof(f46,plain,
! [X0,X1] : quotient(X1,difference(X0,X1)) = X0,
inference(superposition,[],[f36,f37]) ).
fof(f37,plain,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos02) ).
fof(f8381,plain,
! [X0,X1] : quotient(X0,difference(X1,X0)) = product(product(product(difference(X1,difference(X1,product(X0,difference(X1,X0)))),X1),X0),X0),
inference(superposition,[],[f107,f2294]) ).
fof(f2294,plain,
! [X2,X1] : difference(X1,X2) = product(X2,product(X2,product(difference(X1,difference(X1,product(X2,difference(X1,X2)))),X1))),
inference(forward_demodulation,[],[f2271,f2156]) ).
fof(f2156,plain,
! [X3,X6,X4,X5] : product(X5,product(difference(X3,X4),X6)) = product(X4,product(difference(X3,X5),X6)),
inference(superposition,[],[f721,f37]) ).
fof(f721,plain,
! [X3,X6,X4,X5] : product(product(X3,X5),product(difference(X3,X4),X6)) = product(X4,product(X5,X6)),
inference(superposition,[],[f42,f37]) ).
fof(f2271,plain,
! [X2,X1] : difference(X1,X2) = product(X2,product(difference(X1,product(X2,difference(X1,X2))),product(difference(X1,X2),X1))),
inference(backward_demodulation,[],[f88,f2156]) ).
fof(f88,plain,
! [X2,X1] : difference(X1,X2) = product(product(X2,difference(X1,X2)),product(difference(X1,X2),product(difference(X1,X2),X1))),
inference(superposition,[],[f39,f37]) ).
fof(f107,plain,
! [X0,X1] : product(product(X0,X1),X1) = quotient(X1,product(X1,product(X1,X0))),
inference(superposition,[],[f36,f39]) ).
fof(f8747,plain,
! [X28,X29] : quotient(X28,product(X28,difference(X29,X28))) = product(X28,product(product(product(difference(X29,difference(X29,product(X28,difference(X29,X28)))),X29),X28),X28)),
inference(forward_demodulation,[],[f8746,f873]) ).
fof(f8746,plain,
! [X28,X29] : quotient(X28,product(X28,difference(X29,X28))) = product(product(X28,product(product(difference(X29,difference(X29,product(X28,difference(X29,X28)))),X29),X28)),X28),
inference(forward_demodulation,[],[f8391,f873]) ).
fof(f8391,plain,
! [X28,X29] : product(product(product(X28,product(difference(X29,difference(X29,product(X28,difference(X29,X28)))),X29)),X28),X28) = quotient(X28,product(X28,difference(X29,X28))),
inference(superposition,[],[f107,f2294]) ).
fof(f9043,plain,
! [X0,X1] : product(product(X0,X1),X1) = product(X1,quotient(X1,product(X1,X0))),
inference(backward_demodulation,[],[f107,f8845]) ).
fof(f34233,plain,
! [X3,X4] : difference(product(X4,X3),X3) = product(difference(product(X3,quotient(X4,X3)),difference(product(X4,X3),X3)),X3),
inference(superposition,[],[f12097,f148]) ).
fof(f12097,plain,
! [X6,X5] : product(X5,X6) = product(difference(X6,product(X5,X6)),X5),
inference(superposition,[],[f10764,f36]) ).
fof(f10764,plain,
! [X2,X1] : product(difference(X2,X1),quotient(X1,X2)) = X1,
inference(superposition,[],[f10482,f46]) ).
fof(f22440,plain,
! [X14,X15] : product(X14,quotient(X15,X14)) = difference(X14,difference(product(X15,X14),X14)),
inference(superposition,[],[f35,f148]) ).
fof(f34833,plain,
! [X3,X4] : product(difference(X4,X3),X4) = difference(X3,product(difference(X4,X3),X3)),
inference(superposition,[],[f12289,f46]) ).
fof(f45699,plain,
! [X0] : product(difference(X0,b),c1) = product(b,product(difference(X0,a),X0)),
inference(forward_demodulation,[],[f45642,f2156]) ).
fof(f45642,plain,
! [X0] : product(difference(X0,b),c1) = product(a,product(difference(X0,b),X0)),
inference(superposition,[],[f851,f45595]) ).
fof(f45595,plain,
! [X0] : c1 = product(difference(difference(X0,b),a),X0),
inference(forward_demodulation,[],[f45594,f2255]) ).
fof(f2255,plain,
! [X18,X19,X17,X20] : product(difference(X17,X19),X20) = difference(product(X17,X18),product(X19,product(X18,X20))),
inference(superposition,[],[f35,f721]) ).
fof(f45594,plain,
! [X0] : c1 = difference(product(difference(X0,b),b),product(a,product(b,X0))),
inference(forward_demodulation,[],[f45557,f35143]) ).
fof(f35143,plain,
! [X6,X7] : product(X7,product(X7,quotient(X6,X7))) = product(difference(X6,X7),X7),
inference(backward_demodulation,[],[f148,f35139]) ).
fof(f45557,plain,
! [X0] : c1 = difference(product(b,product(b,quotient(X0,b))),product(a,product(b,X0))),
inference(superposition,[],[f31258,f3520]) ).
fof(f31258,plain,
! [X6] : c1 = difference(product(b,quotient(X6,b)),product(a,X6)),
inference(superposition,[],[f48,f4160]) ).
fof(f4160,plain,
! [X1] : product(b,quotient(X1,b)) = quotient(product(a,X1),c1),
inference(superposition,[],[f1987,f38]) ).
fof(f1987,plain,
! [X1] : product(b,X1) = quotient(product(a,product(X1,b)),c1),
inference(superposition,[],[f36,f1016]) ).
fof(f1016,plain,
! [X34] : product(a,product(X34,b)) = product(product(b,X34),c1),
inference(forward_demodulation,[],[f1015,f742]) ).
fof(f1015,plain,
! [X34] : product(a,product(X34,b)) = product(product(b,c1),product(X34,c1)),
inference(forward_demodulation,[],[f889,f735]) ).
fof(f735,plain,
! [X46,X45] : product(product(a,X45),product(b,X46)) = product(product(b,c1),product(X45,X46)),
inference(superposition,[],[f42,f56]) ).
fof(f56,plain,
product(a,b) = product(b,c1),
inference(resolution,[],[f41,f29]) ).
fof(f29,plain,
d(a,b,c1),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
d(a,b,c1),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos12) ).
fof(f889,plain,
! [X34] : product(a,product(X34,b)) = product(product(a,X34),product(b,c1)),
inference(superposition,[],[f720,f56]) ).
fof(f851,plain,
! [X2,X3,X4] : product(X2,product(difference(X2,X3),X4)) = product(X3,product(X2,X4)),
inference(superposition,[],[f720,f37]) ).
fof(f59104,plain,
product(a2,b) = product(b,product(a,quotient(b2,a))),
inference(backward_demodulation,[],[f58812,f59103]) ).
fof(f59103,plain,
quotient(product(c1,b2),b) = product(a,quotient(b2,a)),
inference(forward_demodulation,[],[f59096,f58337]) ).
fof(f58337,plain,
product(a,quotient(b2,a)) = product(a2,quotient(b,a2)),
inference(forward_demodulation,[],[f58336,f35304]) ).
fof(f58336,plain,
product(a,quotient(b2,a)) = product(difference(b,a2),b),
inference(forward_demodulation,[],[f58335,f4093]) ).
fof(f4093,plain,
! [X0] : product(difference(b,X0),b) = difference(a,product(X0,c1)),
inference(superposition,[],[f35,f1983]) ).
fof(f1983,plain,
! [X0] : product(X0,c1) = product(a,product(difference(b,X0),b)),
inference(superposition,[],[f1016,f37]) ).
fof(f58335,plain,
difference(a,product(a2,c1)) = product(a,quotient(b2,a)),
inference(forward_demodulation,[],[f58331,f58305]) ).
fof(f58305,plain,
quotient(product(a2,c1),difference(b2,a)) = product(a,quotient(b2,a)),
inference(forward_demodulation,[],[f58304,f35145]) ).
fof(f58304,plain,
quotient(product(a2,c1),difference(b2,a)) = difference(a,product(difference(b2,a),a)),
inference(forward_demodulation,[],[f58276,f12289]) ).
fof(f58276,plain,
product(difference(b2,a),quotient(a,difference(b2,a))) = quotient(product(a2,c1),difference(b2,a)),
inference(superposition,[],[f3520,f58135]) ).
fof(f58135,plain,
product(a2,c1) = product(difference(b2,a),a),
inference(forward_demodulation,[],[f57817,f45998]) ).
fof(f45998,plain,
product(a2,c1) = difference(product(b,a1),a),
inference(forward_demodulation,[],[f45997,f9039]) ).
fof(f9039,plain,
product(a2,c1) = product(c1,difference(b1,a2)),
inference(forward_demodulation,[],[f8841,f2654]) ).
fof(f2654,plain,
product(a2,c1) = quotient(c1,product(c1,b1)),
inference(superposition,[],[f36,f2570]) ).
fof(f2570,plain,
c1 = product(product(a2,c1),product(c1,b1)),
inference(forward_demodulation,[],[f2569,f34]) ).
fof(f2569,plain,
c1 = product(product(a2,c1),product(product(c1,b1),product(c1,b1))),
inference(forward_demodulation,[],[f2548,f42]) ).
fof(f2548,plain,
c1 = product(product(a2,product(c1,b1)),product(c1,product(c1,b1))),
inference(superposition,[],[f39,f1032]) ).
fof(f8841,plain,
product(c1,difference(b1,a2)) = quotient(c1,product(c1,b1)),
inference(superposition,[],[f8748,f2586]) ).
fof(f2586,plain,
b1 = difference(difference(b1,a2),c1),
inference(superposition,[],[f35,f2571]) ).
fof(f2571,plain,
c1 = product(difference(b1,a2),b1),
inference(forward_demodulation,[],[f2549,f2255]) ).
fof(f2549,plain,
! [X0] : c1 = difference(product(b1,X0),product(a2,product(X0,b1))),
inference(superposition,[],[f35,f1032]) ).
fof(f45997,plain,
product(c1,difference(b1,a2)) = difference(product(b,a1),a),
inference(forward_demodulation,[],[f45996,f2587]) ).
fof(f2587,plain,
difference(b1,a2) = quotient(c1,b1),
inference(superposition,[],[f36,f2571]) ).
fof(f45996,plain,
product(c1,quotient(c1,b1)) = difference(product(b,a1),a),
inference(forward_demodulation,[],[f45981,f8845]) ).
fof(f45981,plain,
quotient(c1,product(c1,b1)) = difference(product(b,a1),a),
inference(superposition,[],[f45645,f6265]) ).
fof(f6265,plain,
product(b,a1) = difference(product(c1,b1),b),
inference(superposition,[],[f35,f5552]) ).
fof(f5552,plain,
b = product(product(c1,b1),product(b,a1)),
inference(forward_demodulation,[],[f5551,f34]) ).
fof(f5551,plain,
b = product(product(c1,b1),product(product(b,b),a1)),
inference(forward_demodulation,[],[f5550,f2972]) ).
fof(f2972,plain,
! [X82,X83,X81,X84,X85] : product(product(X81,X85),product(product(X83,X82),X84)) = product(product(X81,X82),product(product(X83,difference(X82,X85)),X84)),
inference(forward_demodulation,[],[f2971,f42]) ).
fof(f2971,plain,
! [X82,X83,X81,X84,X85] : product(product(X81,X85),product(product(X83,X82),X84)) = product(product(X81,product(X83,difference(X82,X85))),product(X82,X84)),
inference(forward_demodulation,[],[f2970,f2776]) ).
fof(f2776,plain,
! [X3,X6,X4,X5] : product(X5,product(X6,difference(X3,X4))) = product(product(quotient(X5,X3),X6),X4),
inference(superposition,[],[f731,f37]) ).
fof(f731,plain,
! [X38,X36,X37,X35] : product(product(quotient(X35,X36),X37),product(X36,X38)) = product(X35,product(X37,X38)),
inference(superposition,[],[f42,f38]) ).
fof(f2970,plain,
! [X82,X83,X81,X84,X85] : product(product(product(quotient(X81,X82),X83),X85),product(X82,X84)) = product(product(X81,X85),product(product(X83,X82),X84)),
inference(forward_demodulation,[],[f2846,f1748]) ).
fof(f1748,plain,
! [X31,X28,X29,X32,X30] : product(product(X31,product(X28,X29)),product(X32,product(X30,X29))) = product(product(X31,X32),product(product(X28,X30),X29)),
inference(superposition,[],[f42,f742]) ).
fof(f2846,plain,
! [X82,X83,X81,X84,X85] : product(product(product(quotient(X81,X82),X83),X85),product(X82,X84)) = product(product(X81,product(X83,X84)),product(X85,product(X82,X84))),
inference(superposition,[],[f742,f731]) ).
fof(f5550,plain,
b = product(product(c1,b),product(product(b,difference(b,b1)),a1)),
inference(forward_demodulation,[],[f5549,f42]) ).
fof(f5549,plain,
b = product(product(c1,product(b,difference(b,b1))),product(b,a1)),
inference(forward_demodulation,[],[f5548,f3864]) ).
fof(f3864,plain,
! [X91,X92] : product(product(difference(b,a),X91),X92) = product(c1,product(X91,difference(b,X92))),
inference(superposition,[],[f743,f2362]) ).
fof(f2362,plain,
c1 = product(difference(b,a),b),
inference(backward_demodulation,[],[f1986,f2255]) ).
fof(f1986,plain,
! [X0] : c1 = difference(product(b,X0),product(a,product(X0,b))),
inference(superposition,[],[f35,f1016]) ).
fof(f743,plain,
! [X3,X6,X4,X5] : product(product(X5,X3),product(X6,difference(X3,X4))) = product(product(X5,X6),X4),
inference(superposition,[],[f42,f37]) ).
fof(f5548,plain,
b = product(product(product(difference(b,a),b),b1),product(b,a1)),
inference(forward_demodulation,[],[f5547,f5519]) ).
fof(f5519,plain,
difference(b,a) = product(difference(c1,a),c1),
inference(superposition,[],[f35,f5507]) ).
fof(f5507,plain,
a = product(b,product(difference(c1,a),c1)),
inference(backward_demodulation,[],[f4669,f5505]) ).
fof(f5505,plain,
! [X10] : product(product(b1,a1),product(a,X10)) = product(b,product(difference(c1,a),X10)),
inference(forward_demodulation,[],[f5482,f2156]) ).
fof(f5482,plain,
! [X10] : product(a,product(difference(c1,b),X10)) = product(product(b1,a1),product(a,X10)),
inference(superposition,[],[f720,f5162]) ).
fof(f5162,plain,
product(b1,a1) = product(a,difference(c1,b)),
inference(backward_demodulation,[],[f5056,f5124]) ).
fof(f5124,plain,
product(b1,a1) = product(b,a),
inference(forward_demodulation,[],[f5106,f5072]) ).
fof(f5072,plain,
product(b,a) = quotient(a,product(a,c1)),
inference(superposition,[],[f36,f4567]) ).
fof(f4567,plain,
a = product(product(b,a),product(a,c1)),
inference(forward_demodulation,[],[f4566,f34]) ).
fof(f4566,plain,
a = product(product(b,a),product(a,product(c1,c1))),
inference(forward_demodulation,[],[f4564,f35]) ).
fof(f4564,plain,
a = product(product(b,a),product(a,product(difference(a1,product(a1,c1)),c1))),
inference(backward_demodulation,[],[f4147,f4545]) ).
fof(f4545,plain,
product(a1,c1) = product(a,c),
inference(forward_demodulation,[],[f4526,f38]) ).
fof(f4526,plain,
product(a1,c1) = product(a,product(quotient(c,b),b)),
inference(superposition,[],[f1016,f4521]) ).
fof(f4521,plain,
a1 = product(b,quotient(c,b)),
inference(forward_demodulation,[],[f4475,f36]) ).
fof(f4475,plain,
product(b,quotient(c,b)) = quotient(product(a1,b),b),
inference(superposition,[],[f3520,f59]) ).
fof(f59,plain,
product(a1,b) = product(b,c),
inference(resolution,[],[f41,f32]) ).
fof(f32,plain,
d(a1,b,c),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
d(a1,b,c),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos10) ).
fof(f4147,plain,
a = product(product(b,a),product(a,product(difference(a1,product(a,c)),c1))),
inference(forward_demodulation,[],[f4146,f2156]) ).
fof(f4146,plain,
a = product(product(b,a),product(product(a,c),product(difference(a1,a),c1))),
inference(forward_demodulation,[],[f4145,f42]) ).
fof(f4145,plain,
a = product(product(b,a),product(product(a,difference(a1,a)),product(c,c1))),
inference(forward_demodulation,[],[f4144,f42]) ).
fof(f4144,plain,
a = product(product(b,product(a,difference(a1,a))),product(a,product(c,c1))),
inference(forward_demodulation,[],[f4129,f2776]) ).
fof(f4129,plain,
a = product(product(product(quotient(b,a1),a),a),product(a,product(c,c1))),
inference(superposition,[],[f39,f4092]) ).
fof(f4092,plain,
product(c,c1) = product(a,quotient(b,a1)),
inference(superposition,[],[f1983,f447]) ).
fof(f447,plain,
product(difference(b,c),b) = quotient(b,a1),
inference(superposition,[],[f36,f433]) ).
fof(f433,plain,
b = product(product(difference(b,c),b),a1),
inference(forward_demodulation,[],[f428,f44]) ).
fof(f44,plain,
! [X0] : quotient(X0,X0) = X0,
inference(superposition,[],[f36,f34]) ).
fof(f428,plain,
quotient(b,b) = product(product(difference(b,c),b),a1),
inference(superposition,[],[f36,f400]) ).
fof(f400,plain,
b = product(product(product(difference(b,c),b),a1),b),
inference(forward_demodulation,[],[f399,f34]) ).
fof(f399,plain,
b = product(product(product(difference(b,c),b),a1),product(b,b)),
inference(forward_demodulation,[],[f358,f42]) ).
fof(f358,plain,
b = product(product(product(difference(b,c),b),b),product(a1,b)),
inference(superposition,[],[f98,f59]) ).
fof(f98,plain,
! [X2,X1] : product(product(product(difference(X1,X2),X1),X1),product(X1,X2)) = X1,
inference(superposition,[],[f39,f37]) ).
fof(f5106,plain,
product(b1,a1) = quotient(a,product(a,c1)),
inference(superposition,[],[f36,f4669]) ).
fof(f5056,plain,
product(b,a) = product(a,difference(c1,b)),
inference(superposition,[],[f38,f4514]) ).
fof(f4514,plain,
a = quotient(product(b,a),difference(c1,b)),
inference(forward_demodulation,[],[f4513,f2002]) ).
fof(f2002,plain,
a = product(difference(c1,b),c1),
inference(forward_demodulation,[],[f2001,f34]) ).
fof(f2001,plain,
product(difference(c1,b),c1) = product(a,a),
inference(forward_demodulation,[],[f1981,f38]) ).
fof(f1981,plain,
product(difference(c1,b),c1) = product(a,product(quotient(a,b),b)),
inference(superposition,[],[f1016,f240]) ).
fof(f240,plain,
product(b,quotient(a,b)) = difference(c1,b),
inference(superposition,[],[f35,f228]) ).
fof(f228,plain,
b = product(c1,product(b,quotient(a,b))),
inference(forward_demodulation,[],[f225,f43]) ).
fof(f43,plain,
! [X0] : difference(X0,X0) = X0,
inference(superposition,[],[f35,f34]) ).
fof(f225,plain,
product(c1,product(b,quotient(a,b))) = difference(b,b),
inference(superposition,[],[f35,f155]) ).
fof(f155,plain,
b = product(b,product(c1,product(b,quotient(a,b)))),
inference(forward_demodulation,[],[f154,f34]) ).
fof(f154,plain,
b = product(product(b,b),product(c1,product(b,quotient(a,b)))),
inference(forward_demodulation,[],[f132,f42]) ).
fof(f132,plain,
b = product(product(b,c1),product(b,product(b,quotient(a,b)))),
inference(superposition,[],[f90,f56]) ).
fof(f4513,plain,
product(difference(c1,b),c1) = quotient(product(b,a),difference(c1,b)),
inference(forward_demodulation,[],[f4454,f46]) ).
fof(f4454,plain,
product(difference(c1,b),quotient(b,difference(c1,b))) = quotient(product(b,a),difference(c1,b)),
inference(superposition,[],[f3520,f1150]) ).
fof(f1150,plain,
product(b,a) = product(difference(c1,b),b),
inference(forward_demodulation,[],[f1114,f38]) ).
fof(f1114,plain,
product(b,product(quotient(a,b),b)) = product(difference(c1,b),b),
inference(superposition,[],[f873,f240]) ).
fof(f4669,plain,
a = product(product(b1,a1),product(a,c1)),
inference(forward_demodulation,[],[f4668,f42]) ).
fof(f4668,plain,
a = product(product(b1,a),product(a1,c1)),
inference(forward_demodulation,[],[f4667,f34]) ).
fof(f4667,plain,
a = product(product(b1,a),product(product(a1,a1),c1)),
inference(backward_demodulation,[],[f4664,f4666]) ).
fof(f4666,plain,
! [X8] : product(a,product(X8,quotient(b,a1))) = product(product(a1,X8),c1),
inference(forward_demodulation,[],[f4665,f742]) ).
fof(f4665,plain,
! [X8] : product(a,product(X8,quotient(b,a1))) = product(product(a1,c1),product(X8,c1)),
inference(backward_demodulation,[],[f4136,f4647]) ).
fof(f4647,plain,
! [X2,X3] : product(product(a1,c1),product(X2,X3)) = product(product(a,X2),product(c,X3)),
inference(superposition,[],[f42,f4545]) ).
fof(f4136,plain,
! [X8] : product(a,product(X8,quotient(b,a1))) = product(product(a,X8),product(c,c1)),
inference(superposition,[],[f720,f4092]) ).
fof(f4664,plain,
a = product(product(b1,a),product(a,product(a1,quotient(b,a1)))),
inference(forward_demodulation,[],[f4663,f4136]) ).
fof(f4663,plain,
a = product(product(b1,a),product(product(a,a1),product(c,c1))),
inference(forward_demodulation,[],[f4662,f42]) ).
fof(f4662,plain,
a = product(product(b1,a),product(product(a,c),product(a1,c1))),
inference(forward_demodulation,[],[f4661,f42]) ).
fof(f4661,plain,
a = product(product(b1,product(a,c)),product(a,product(a1,c1))),
inference(forward_demodulation,[],[f4645,f2236]) ).
fof(f2236,plain,
! [X2] : product(b1,product(X2,c)) = product(product(c,X2),a),
inference(superposition,[],[f721,f2091]) ).
fof(f2091,plain,
a = product(difference(c,b1),c),
inference(forward_demodulation,[],[f2090,f34]) ).
fof(f2090,plain,
product(difference(c,b1),c) = product(a,a),
inference(forward_demodulation,[],[f2068,f38]) ).
fof(f2068,plain,
product(difference(c,b1),c) = product(a,product(quotient(a,b1),b1)),
inference(superposition,[],[f1024,f279]) ).
fof(f279,plain,
product(b1,quotient(a,b1)) = difference(c,b1),
inference(superposition,[],[f35,f267]) ).
fof(f267,plain,
b1 = product(c,product(b1,quotient(a,b1))),
inference(forward_demodulation,[],[f264,f43]) ).
fof(f264,plain,
product(c,product(b1,quotient(a,b1))) = difference(b1,b1),
inference(superposition,[],[f35,f157]) ).
fof(f157,plain,
b1 = product(b1,product(c,product(b1,quotient(a,b1)))),
inference(forward_demodulation,[],[f156,f34]) ).
fof(f156,plain,
b1 = product(product(b1,b1),product(c,product(b1,quotient(a,b1)))),
inference(forward_demodulation,[],[f133,f42]) ).
fof(f133,plain,
b1 = product(product(b1,c),product(b1,product(b1,quotient(a,b1)))),
inference(superposition,[],[f90,f58]) ).
fof(f58,plain,
product(a,b1) = product(b1,c),
inference(resolution,[],[f41,f30]) ).
fof(f30,plain,
d(a,b1,c),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
d(a,b1,c),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos11) ).
fof(f1024,plain,
! [X35] : product(a,product(X35,b1)) = product(product(b1,X35),c),
inference(forward_demodulation,[],[f1023,f742]) ).
fof(f1023,plain,
! [X35] : product(a,product(X35,b1)) = product(product(b1,c),product(X35,c)),
inference(forward_demodulation,[],[f890,f736]) ).
fof(f736,plain,
! [X48,X47] : product(product(a,X47),product(b1,X48)) = product(product(b1,c),product(X47,X48)),
inference(superposition,[],[f42,f58]) ).
fof(f890,plain,
! [X35] : product(a,product(X35,b1)) = product(product(a,X35),product(b1,c)),
inference(superposition,[],[f720,f58]) ).
fof(f4645,plain,
a = product(product(product(c,a),a),product(a,product(a1,c1))),
inference(superposition,[],[f39,f4545]) ).
fof(f5547,plain,
b = product(product(product(product(difference(c1,a),c1),b),b1),product(b,a1)),
inference(forward_demodulation,[],[f5546,f42]) ).
fof(f5546,plain,
b = product(product(product(product(difference(c1,a),c1),b),b),product(b1,a1)),
inference(forward_demodulation,[],[f5522,f5199]) ).
fof(f5199,plain,
! [X0,X1] : product(product(X0,b),product(X1,a)) = product(product(X0,X1),product(b1,a1)),
inference(superposition,[],[f42,f5124]) ).
fof(f5522,plain,
b = product(product(product(product(difference(c1,a),c1),b),b),product(b,a)),
inference(superposition,[],[f39,f5507]) ).
fof(f45645,plain,
! [X4] : difference(difference(X4,b),a) = quotient(c1,X4),
inference(superposition,[],[f36,f45595]) ).
fof(f57817,plain,
difference(product(b,a1),a) = product(difference(b2,a),a),
inference(superposition,[],[f35139,f47031]) ).
fof(f47031,plain,
product(b,a1) = product(b2,a),
inference(forward_demodulation,[],[f46991,f37]) ).
fof(f46991,plain,
product(b2,a) = product(b,product(b2,difference(b2,a1))),
inference(superposition,[],[f851,f46389]) ).
fof(f46389,plain,
a = product(difference(b2,b),difference(b2,a1)),
inference(superposition,[],[f45988,f4595]) ).
fof(f4595,plain,
quotient(c1,b2) = difference(b2,a1),
inference(superposition,[],[f35,f4522]) ).
fof(f4522,plain,
a1 = product(b2,quotient(c1,b2)),
inference(forward_demodulation,[],[f4490,f36]) ).
fof(f4490,plain,
product(b2,quotient(c1,b2)) = quotient(product(a1,b2),b2),
inference(superposition,[],[f3520,f57]) ).
fof(f57,plain,
product(a1,b2) = product(b2,c1),
inference(resolution,[],[f41,f31]) ).
fof(f31,plain,
d(a1,b2,c1),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
d(a1,b2,c1),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos14) ).
fof(f45988,plain,
! [X1] : a = product(difference(X1,b),quotient(c1,X1)),
inference(superposition,[],[f37,f45645]) ).
fof(f58331,plain,
difference(a,product(a2,c1)) = quotient(product(a2,c1),difference(b2,a)),
inference(superposition,[],[f12146,f58248]) ).
fof(f58248,plain,
a = difference(difference(b2,a),product(a2,c1)),
inference(superposition,[],[f35,f58135]) ).
fof(f12146,plain,
! [X6,X7] : quotient(X7,X6) = difference(difference(X6,X7),X7),
inference(superposition,[],[f35,f10764]) ).
fof(f59096,plain,
quotient(product(c1,b2),b) = product(a2,quotient(b,a2)),
inference(backward_demodulation,[],[f47539,f58584]) ).
fof(f58584,plain,
! [X31,X32] : product(X31,quotient(quotient(X31,X32),X31)) = product(X32,quotient(X31,X32)),
inference(superposition,[],[f35304,f48]) ).
fof(f47539,plain,
product(b,quotient(quotient(b,a2),b)) = quotient(product(c1,b2),b),
inference(superposition,[],[f3520,f46954]) ).
fof(f46954,plain,
product(c1,b2) = product(b,quotient(b,a2)),
inference(forward_demodulation,[],[f46930,f46802]) ).
fof(f46802,plain,
product(c1,b2) = quotient(b,product(b1,a)),
inference(forward_demodulation,[],[f46801,f11280]) ).
fof(f11280,plain,
product(c1,b2) = product(difference(a1,c1),c1),
inference(backward_demodulation,[],[f11037,f11219]) ).
fof(f11219,plain,
quotient(b2,a1) = difference(a1,c1),
inference(superposition,[],[f35,f11036]) ).
fof(f11036,plain,
c1 = product(a1,quotient(b2,a1)),
inference(forward_demodulation,[],[f11018,f3520]) ).
fof(f11018,plain,
c1 = quotient(product(a1,b2),a1),
inference(superposition,[],[f36,f10874]) ).
fof(f10874,plain,
product(a1,b2) = product(c1,a1),
inference(forward_demodulation,[],[f10782,f36]) ).
fof(f10782,plain,
product(a1,b2) = product(c1,quotient(product(a1,b2),b2)),
inference(superposition,[],[f10482,f65]) ).
fof(f65,plain,
b2 = quotient(product(a1,b2),c1),
inference(superposition,[],[f36,f57]) ).
fof(f11037,plain,
product(c1,b2) = product(quotient(b2,a1),c1),
inference(backward_demodulation,[],[f4512,f11036]) ).
fof(f4512,plain,
product(quotient(b2,a1),c1) = product(product(a1,quotient(b2,a1)),b2),
inference(forward_demodulation,[],[f4511,f742]) ).
fof(f4511,plain,
product(quotient(b2,a1),c1) = product(product(a1,b2),product(quotient(b2,a1),b2)),
inference(forward_demodulation,[],[f4510,f629]) ).
fof(f629,plain,
quotient(b2,product(a1,b2)) = product(quotient(b2,a1),b2),
inference(superposition,[],[f46,f617]) ).
fof(f617,plain,
product(a1,b2) = difference(product(quotient(b2,a1),b2),b2),
inference(forward_demodulation,[],[f616,f57]) ).
fof(f616,plain,
product(b2,c1) = difference(product(quotient(b2,a1),b2),b2),
inference(forward_demodulation,[],[f598,f37]) ).
fof(f598,plain,
product(b2,product(b2,difference(b2,c1))) = difference(product(quotient(b2,a1),b2),b2),
inference(superposition,[],[f108,f493]) ).
fof(f493,plain,
product(difference(b2,c1),b2) = quotient(b2,a1),
inference(superposition,[],[f36,f480]) ).
fof(f480,plain,
b2 = product(product(difference(b2,c1),b2),a1),
inference(forward_demodulation,[],[f475,f44]) ).
fof(f475,plain,
product(product(difference(b2,c1),b2),a1) = quotient(b2,b2),
inference(superposition,[],[f36,f405]) ).
fof(f405,plain,
b2 = product(product(product(difference(b2,c1),b2),a1),b2),
inference(forward_demodulation,[],[f404,f34]) ).
fof(f404,plain,
b2 = product(product(product(difference(b2,c1),b2),a1),product(b2,b2)),
inference(forward_demodulation,[],[f366,f42]) ).
fof(f366,plain,
b2 = product(product(product(difference(b2,c1),b2),b2),product(a1,b2)),
inference(superposition,[],[f98,f57]) ).
fof(f108,plain,
! [X2,X3] : product(X3,product(X3,X2)) = difference(product(product(X2,X3),X3),X3),
inference(superposition,[],[f35,f39]) ).
fof(f4510,plain,
product(product(a1,b2),quotient(b2,product(a1,b2))) = product(quotient(b2,a1),c1),
inference(forward_demodulation,[],[f4450,f2834]) ).
fof(f2834,plain,
! [X21,X24,X22,X23] : product(quotient(X21,X22),X23) = quotient(product(X21,product(X23,X24)),product(X22,X24)),
inference(superposition,[],[f36,f731]) ).
fof(f4450,plain,
product(product(a1,b2),quotient(b2,product(a1,b2))) = quotient(product(b2,product(c1,b2)),product(a1,b2)),
inference(superposition,[],[f3520,f1121]) ).
fof(f1121,plain,
product(b2,product(c1,b2)) = product(product(a1,b2),b2),
inference(superposition,[],[f873,f57]) ).
fof(f46801,plain,
product(difference(a1,c1),c1) = quotient(b,product(b1,a)),
inference(forward_demodulation,[],[f46779,f35139]) ).
fof(f46779,plain,
difference(product(a1,c1),c1) = quotient(b,product(b1,a)),
inference(superposition,[],[f46152,f9035]) ).
fof(f9035,plain,
product(b1,a) = quotient(a,product(a1,c1)),
inference(forward_demodulation,[],[f9034,f5062]) ).
fof(f5062,plain,
product(b1,a) = product(a,difference(c,b1)),
inference(superposition,[],[f38,f4518]) ).
fof(f4518,plain,
a = quotient(product(b1,a),difference(c,b1)),
inference(forward_demodulation,[],[f4517,f2091]) ).
fof(f4517,plain,
product(difference(c,b1),c) = quotient(product(b1,a),difference(c,b1)),
inference(forward_demodulation,[],[f4461,f46]) ).
fof(f4461,plain,
product(difference(c,b1),quotient(b1,difference(c,b1))) = quotient(product(b1,a),difference(c,b1)),
inference(superposition,[],[f3520,f1152]) ).
fof(f1152,plain,
product(b1,a) = product(difference(c,b1),b1),
inference(forward_demodulation,[],[f1118,f38]) ).
fof(f1118,plain,
product(b1,product(quotient(a,b1),b1)) = product(difference(c,b1),b1),
inference(superposition,[],[f873,f279]) ).
fof(f9034,plain,
product(a,difference(c,b1)) = quotient(a,product(a1,c1)),
inference(forward_demodulation,[],[f8838,f4545]) ).
fof(f8838,plain,
product(a,difference(c,b1)) = quotient(a,product(a,c)),
inference(superposition,[],[f8748,f2103]) ).
fof(f2103,plain,
c = difference(difference(c,b1),a),
inference(superposition,[],[f35,f2091]) ).
fof(f46152,plain,
! [X3] : quotient(b,quotient(a,X3)) = difference(X3,c1),
inference(superposition,[],[f35,f45875]) ).
fof(f45875,plain,
! [X2] : c1 = product(X2,quotient(b,quotient(a,X2))),
inference(superposition,[],[f45640,f48]) ).
fof(f45640,plain,
! [X2] : c1 = product(difference(X2,a),quotient(b,X2)),
inference(superposition,[],[f45595,f48]) ).
fof(f46930,plain,
quotient(b,product(b1,a)) = product(b,quotient(b,a2)),
inference(superposition,[],[f8845,f46861]) ).
fof(f46861,plain,
product(b1,a) = product(b,a2),
inference(forward_demodulation,[],[f46821,f37]) ).
fof(f46821,plain,
product(b1,a) = product(b,product(b1,difference(b1,a2))),
inference(superposition,[],[f851,f46388]) ).
fof(f46388,plain,
a = product(difference(b1,b),difference(b1,a2)),
inference(superposition,[],[f45988,f2587]) ).
fof(f58812,plain,
product(a2,b) = product(b,quotient(product(c1,b2),b)),
inference(forward_demodulation,[],[f58811,f47501]) ).
fof(f47501,plain,
product(a2,b) = product(product(b1,c1),product(a,b2)),
inference(forward_demodulation,[],[f47500,f42]) ).
fof(f47500,plain,
product(a2,b) = product(product(b1,a),product(c1,b2)),
inference(forward_demodulation,[],[f47499,f35]) ).
fof(f47499,plain,
product(product(b1,a),product(c1,b2)) = difference(b,product(b,product(a2,b))),
inference(forward_demodulation,[],[f47471,f46927]) ).
fof(f46927,plain,
product(b,product(a2,b)) = product(product(b1,a),b),
inference(superposition,[],[f873,f46861]) ).
fof(f47471,plain,
product(product(b1,a),product(c1,b2)) = difference(b,product(product(b1,a),b)),
inference(superposition,[],[f12289,f46802]) ).
fof(f58811,plain,
product(product(b1,c1),product(a,b2)) = product(b,quotient(product(c1,b2),b)),
inference(forward_demodulation,[],[f58492,f42]) ).
fof(f58492,plain,
product(product(b1,a),product(c1,b2)) = product(b,quotient(product(c1,b2),b)),
inference(superposition,[],[f35304,f47464]) ).
fof(f47464,plain,
product(b1,a) = difference(product(c1,b2),b),
inference(superposition,[],[f48,f46802]) ).
fof(f62874,plain,
product(b,quotient(b,b1)) = product(product(b1,quotient(b,b1)),b),
inference(forward_demodulation,[],[f62873,f10566]) ).
fof(f10566,plain,
! [X40,X38,X39] : product(product(X39,X40),X38) = product(X38,product(X40,quotient(X38,X39))),
inference(forward_demodulation,[],[f10565,f720]) ).
fof(f10565,plain,
! [X40,X38,X39] : product(product(X38,X40),product(X38,quotient(X38,X39))) = product(product(X39,X40),X38),
inference(forward_demodulation,[],[f10564,f34]) ).
fof(f10564,plain,
! [X40,X38,X39] : product(product(X38,X40),product(X38,quotient(X38,X39))) = product(product(product(X39,X39),X40),X38),
inference(forward_demodulation,[],[f10563,f34]) ).
fof(f10563,plain,
! [X40,X38,X39] : product(product(X38,X40),product(X38,quotient(X38,X39))) = product(product(product(X39,X39),X40),product(X38,X38)),
inference(forward_demodulation,[],[f10562,f1795]) ).
fof(f1795,plain,
! [X8,X6,X9,X7,X5] : product(product(product(X5,X6),X9),product(X7,X8)) = product(product(product(X5,X7),X9),product(product(X6,X7),X8)),
inference(backward_demodulation,[],[f1675,f1748]) ).
fof(f1675,plain,
! [X8,X6,X9,X7,X5] : product(product(product(X5,X6),X9),product(X7,X8)) = product(product(product(X5,X7),product(X6,X8)),product(X9,product(X7,X8))),
inference(superposition,[],[f742,f42]) ).
fof(f10562,plain,
! [X40,X38,X39] : product(product(X38,X40),product(X38,quotient(X38,X39))) = product(product(product(X39,X38),X40),product(product(X39,X38),X38)),
inference(forward_demodulation,[],[f10335,f10327]) ).
fof(f10327,plain,
! [X10,X11,X12,X13] : product(product(X12,X10),product(X13,product(X10,quotient(X10,X11)))) = product(product(X12,X13),product(product(X11,X10),X10)),
inference(superposition,[],[f42,f9131]) ).
fof(f10335,plain,
! [X40,X38,X39] : product(product(X38,X40),product(X38,quotient(X38,X39))) = product(product(product(X39,X38),X38),product(X40,product(X38,quotient(X38,X39)))),
inference(superposition,[],[f742,f9131]) ).
fof(f62873,plain,
product(b,quotient(b,b1)) = product(b,product(quotient(b,b1),quotient(b,b1))),
inference(forward_demodulation,[],[f62872,f862]) ).
fof(f862,plain,
! [X28,X29,X30] : product(quotient(X28,X29),product(X29,X30)) = product(X28,product(quotient(X28,X29),X30)),
inference(superposition,[],[f720,f38]) ).
fof(f62872,plain,
product(quotient(b,b1),product(b1,quotient(b,b1))) = product(b,quotient(b,b1)),
inference(forward_demodulation,[],[f62802,f62776]) ).
fof(f62776,plain,
quotient(b,b1) = difference(b1,difference(b2,b)),
inference(superposition,[],[f36,f61579]) ).
fof(f61579,plain,
b = product(difference(b1,difference(b2,b)),b1),
inference(forward_demodulation,[],[f61539,f35]) ).
fof(f61539,plain,
product(difference(b1,difference(b2,b)),b1) = difference(a2,product(a2,b)),
inference(superposition,[],[f4304,f59109]) ).
fof(f4304,plain,
! [X0] : product(difference(b1,X0),b1) = difference(a2,product(X0,c1)),
inference(superposition,[],[f35,f2546]) ).
fof(f2546,plain,
! [X0] : product(X0,c1) = product(a2,product(difference(b1,X0),b1)),
inference(superposition,[],[f1032,f37]) ).
fof(f62802,plain,
product(difference(b1,difference(b2,b)),product(b1,difference(b1,difference(b2,b)))) = product(b,difference(b1,difference(b2,b))),
inference(superposition,[],[f873,f61579]) ).
fof(f64657,plain,
product(b1,b2) != product(difference(b2,b),b),
inference(forward_demodulation,[],[f64655,f58772]) ).
fof(f58772,plain,
! [X8,X7] : product(difference(X8,X7),X7) = product(X7,product(difference(X8,X7),X8)),
inference(forward_demodulation,[],[f58771,f35143]) ).
fof(f58771,plain,
! [X8,X7] : product(X7,product(X7,quotient(X8,X7))) = product(X7,product(difference(X8,X7),X8)),
inference(forward_demodulation,[],[f58770,f3520]) ).
fof(f58770,plain,
! [X8,X7] : product(X7,quotient(product(X7,X8),X7)) = product(X7,product(difference(X8,X7),X8)),
inference(forward_demodulation,[],[f58769,f34]) ).
fof(f58769,plain,
! [X8,X7] : product(X7,quotient(product(X7,X8),X7)) = product(X7,product(difference(X8,product(X7,X7)),X8)),
inference(forward_demodulation,[],[f58768,f2156]) ).
fof(f58768,plain,
! [X8,X7] : product(X7,quotient(product(X7,X8),X7)) = product(product(X7,X7),product(difference(X8,X7),X8)),
inference(forward_demodulation,[],[f58484,f42]) ).
fof(f58484,plain,
! [X8,X7] : product(X7,quotient(product(X7,X8),X7)) = product(product(X7,difference(X8,X7)),product(X7,X8)),
inference(superposition,[],[f35304,f8863]) ).
fof(f8863,plain,
! [X6,X7] : product(X6,difference(X7,X6)) = difference(product(X6,X7),X6),
inference(superposition,[],[f48,f8748]) ).
fof(f64655,plain,
product(b1,b2) != product(b,product(difference(b2,b),b2)),
inference(backward_demodulation,[],[f444,f64606]) ).
fof(f64606,plain,
! [X10] : product(b,product(difference(b2,b),X10)) = product(product(b1,b),product(b,X10)),
inference(superposition,[],[f720,f64262]) ).
fof(f64262,plain,
product(b1,b) = product(b,difference(b2,b)),
inference(superposition,[],[f38,f62898]) ).
fof(f62898,plain,
b = quotient(product(b1,b),difference(b2,b)),
inference(superposition,[],[f12288,f61583]) ).
fof(f12288,plain,
! [X6,X5] : quotient(product(X5,X6),product(X5,quotient(X6,X5))) = X6,
inference(forward_demodulation,[],[f12234,f35]) ).
fof(f12234,plain,
! [X6,X5] : difference(X5,product(X5,X6)) = quotient(product(X5,X6),product(X5,quotient(X6,X5))),
inference(superposition,[],[f10816,f3520]) ).
fof(f444,plain,
product(b1,b2) != product(product(b1,b),product(b,b2)),
inference(resolution,[],[f40,f27]) ).
fof(f27,plain,
~ m(b1,b,b2),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
~ m(b1,b,b2),
inference(flattening,[],[f17]) ).
fof(f17,negated_conjecture,
~ m(b1,b,b2),
inference(negated_conjecture,[],[f16]) ).
fof(f16,conjecture,
m(b1,b,b2),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',goals) ).
fof(f40,plain,
! [X2,X0,X1] :
( m(X0,X1,X2)
| product(X0,X2) != product(product(X0,X1),product(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( m(X0,X1,X2)
| product(X0,X2) != product(product(X0,X1),product(X1,X2)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( product(X0,X2) = product(product(X0,X1),product(X1,X2))
=> m(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( m(X0,X1,X2)
<=> product(X0,X2) = product(product(X0,X1),product(X1,X2)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X7,X8,X9] :
( m(X7,X8,X9)
<=> product(product(X7,X8),product(X8,X9)) = product(X7,X9) ),
file('/export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938',sos09) ).
fof(f73568,plain,
product(b1,b2) = product(b,quotient(b,b1)),
inference(forward_demodulation,[],[f73567,f62875]) ).
fof(f73567,plain,
product(b1,b2) = product(difference(b2,b),b),
inference(forward_demodulation,[],[f73566,f35143]) ).
fof(f73566,plain,
product(b1,b2) = product(b,product(b,quotient(b2,b))),
inference(forward_demodulation,[],[f73565,f36]) ).
fof(f73565,plain,
product(b,product(b,quotient(b2,b))) = product(b1,quotient(product(b2,b1),b1)),
inference(forward_demodulation,[],[f73564,f3520]) ).
fof(f73564,plain,
product(b1,quotient(product(b2,b1),b1)) = product(b,quotient(product(b,b2),b)),
inference(forward_demodulation,[],[f73527,f4160]) ).
fof(f73527,plain,
product(b1,quotient(product(b2,b1),b1)) = quotient(product(a,product(b,b2)),c1),
inference(superposition,[],[f4346,f60378]) ).
fof(f60378,plain,
product(a,product(b,b2)) = product(a2,product(b2,b1)),
inference(forward_demodulation,[],[f60301,f1032]) ).
fof(f60301,plain,
product(a,product(b,b2)) = product(product(b1,b2),c1),
inference(superposition,[],[f5229,f1778]) ).
fof(f1778,plain,
! [X52] : product(product(X52,b2),c1) = product(product(X52,a1),product(c1,b2)),
inference(forward_demodulation,[],[f1731,f42]) ).
fof(f1731,plain,
! [X52] : product(product(X52,b2),c1) = product(product(X52,c1),product(a1,b2)),
inference(superposition,[],[f742,f57]) ).
fof(f5229,plain,
! [X34] : product(a,product(b,X34)) = product(product(b1,a1),product(c1,X34)),
inference(backward_demodulation,[],[f866,f5200]) ).
fof(f5200,plain,
! [X2,X3] : product(product(b,X2),product(a,X3)) = product(product(b1,a1),product(X2,X3)),
inference(superposition,[],[f42,f5124]) ).
fof(f866,plain,
! [X34] : product(a,product(b,X34)) = product(product(b,c1),product(a,X34)),
inference(superposition,[],[f720,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP778+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 00:52:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.vRIa4iry9s/Vampire---4.8_3938
% 0.14/0.36 % (4056)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (4078)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.21/0.42 % (4059)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.21/0.42 % (4072)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.21/0.42 % (4073)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.21/0.42 % (4066)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.21/0.42 % (4061)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.21/0.42 % (4060)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 28.07/4.35 % (4060)First to succeed.
% 28.07/4.36 % (4060)Refutation found. Thanks to Tanya!
% 28.07/4.36 % SZS status Theorem for Vampire---4
% 28.07/4.36 % SZS output start Proof for Vampire---4
% See solution above
% 28.07/4.36 % (4060)------------------------------
% 28.07/4.36 % (4060)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 28.07/4.36 % (4060)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 28.07/4.36 % (4060)Termination reason: Refutation
% 28.07/4.36
% 28.07/4.36 % (4060)Memory used [KB]: 85329
% 28.07/4.36 % (4060)Time elapsed: 3.936 s
% 28.07/4.36 % (4060)------------------------------
% 28.07/4.36 % (4060)------------------------------
% 28.07/4.36 % (4056)Success in time 3.978 s
% 28.07/4.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------