TSTP Solution File: GRP683+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.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 : Sun May 5 06:10:22 EDT 2024
% Result : Theorem 0.14s 0.51s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 9
% Syntax : Number of formulae : 264 ( 253 unt; 0 def)
% Number of atoms : 277 ( 276 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 22 ~; 9 |; 3 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 624 ( 618 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9071,plain,
$false,
inference(trivial_inequality_removal,[],[f9070]) ).
fof(f9070,plain,
mult(sK0,sK2) != mult(sK0,sK2),
inference(superposition,[],[f9011,f2626]) ).
fof(f2626,plain,
! [X2,X0,X1] : mult(mult(X2,ld(X0,X0)),X1) = mult(X2,X1),
inference(forward_demodulation,[],[f2604,f501]) ).
fof(f501,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[],[f500,f33]) ).
fof(f33,plain,
! [X0] : mult(X0,ld(X0,X0)) = X0,
inference(superposition,[],[f22,f20]) ).
fof(f20,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f22,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f500,plain,
! [X0,X1] : mult(mult(X0,ld(X1,X1)),X1) = mult(X0,mult(X1,ld(X1,X1))),
inference(forward_demodulation,[],[f490,f388]) ).
fof(f388,plain,
! [X2,X0,X1] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(X1,ld(X2,X2))),
inference(forward_demodulation,[],[f387,f135]) ).
fof(f135,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f117,f22]) ).
fof(f117,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,mult(X0,X1))),
inference(superposition,[],[f103,f33]) ).
fof(f103,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(forward_demodulation,[],[f87,f22]) ).
fof(f87,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = ld(X0,mult(X0,mult(X1,X2))),
inference(superposition,[],[f31,f20]) ).
fof(f31,plain,
! [X2,X3,X0,X1] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(mult(X3,ld(X3,X1)),X0),
inference(forward_demodulation,[],[f25,f22]) ).
fof(f25,plain,
! [X2,X3,X0,X1] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X3,X1,X0] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X3,X2))) = mult(ld(X0,mult(X0,X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f387,plain,
! [X2,X0,X1] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(X0,ld(X0,mult(X1,ld(X2,X2))))),
inference(forward_demodulation,[],[f386,f103]) ).
fof(f386,plain,
! [X2,X0,X1] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(mult(X0,ld(X0,X1)),ld(X2,X2))),
inference(forward_demodulation,[],[f385,f349]) ).
fof(f349,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = mult(X1,ld(X0,X0)),
inference(backward_demodulation,[],[f23,f348]) ).
fof(f348,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[],[f321,f303]) ).
fof(f303,plain,
! [X2,X0] : mult(ld(X0,X0),mult(rd(X0,X2),X2)) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[],[f278,f302]) ).
fof(f302,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[],[f301,f135]) ).
fof(f301,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
inference(forward_demodulation,[],[f284,f57]) ).
fof(f57,plain,
! [X0,X1] : mult(X1,ld(X1,ld(X0,X0))) = mult(rd(ld(X1,X1),X0),X0),
inference(backward_demodulation,[],[f30,f51]) ).
fof(f51,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(forward_demodulation,[],[f45,f35]) ).
fof(f35,plain,
! [X0] : ld(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f22,f33]) ).
fof(f45,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f30,f39]) ).
fof(f39,plain,
! [X0] : rd(X0,X0) = mult(rd(rd(X0,X0),X0),X0),
inference(superposition,[],[f23,f37]) ).
fof(f37,plain,
! [X0] : mult(rd(X0,X0),X0) = X0,
inference(superposition,[],[f23,f21]) ).
fof(f21,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f30,plain,
! [X0,X1] : mult(rd(rd(X1,X1),X0),X0) = mult(X1,ld(X1,ld(X0,X0))),
inference(forward_demodulation,[],[f29,f22]) ).
fof(f29,plain,
! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = mult(rd(rd(X1,X1),X0),X0),
inference(forward_demodulation,[],[f24,f23]) ).
fof(f24,plain,
! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f284,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(superposition,[],[f32,f33]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,mult(rd(X2,X0),X0)),
inference(forward_demodulation,[],[f26,f23]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X3,X1,X0] : rd(mult(mult(X0,X1),rd(X3,X2)),rd(X3,X2)) = mult(X0,rd(mult(X1,X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f278,plain,
! [X2,X0,X1] : mult(ld(X0,X0),mult(rd(X0,X2),X2)) = rd(mult(X0,rd(X1,X2)),rd(X1,X2)),
inference(superposition,[],[f32,f56]) ).
fof(f56,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(backward_demodulation,[],[f37,f51]) ).
fof(f321,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(ld(X0,X0),mult(rd(X0,X1),X1)),
inference(superposition,[],[f292,f56]) ).
fof(f292,plain,
! [X2,X0,X1] : mult(X1,mult(rd(X2,X0),X0)) = rd(mult(mult(X1,X2),X0),X0),
inference(superposition,[],[f32,f21]) ).
fof(f23,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f385,plain,
! [X2,X0,X1] : mult(X0,mult(rd(mult(X0,ld(X0,X1)),X2),X2)) = mult(mult(X0,X1),ld(X2,X2)),
inference(forward_demodulation,[],[f326,f348]) ).
fof(f326,plain,
! [X2,X0,X1] : mult(X0,mult(rd(mult(X0,ld(X0,X1)),X2),X2)) = rd(mult(mult(X0,X1),X2),X2),
inference(superposition,[],[f292,f135]) ).
fof(f490,plain,
! [X0,X1] : mult(mult(X0,X1),ld(X1,X1)) = mult(mult(X0,ld(X1,X1)),X1),
inference(superposition,[],[f349,f348]) ).
fof(f2604,plain,
! [X2,X0,X1] : mult(mult(X2,ld(X0,X0)),X1) = mult(mult(X2,ld(X1,X1)),X1),
inference(backward_demodulation,[],[f1250,f2600]) ).
fof(f2600,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = mult(X2,mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f2599,f1746]) ).
fof(f1746,plain,
! [X0,X1] : ld(X0,X1) = ld(ld(X0,X0),ld(X0,X1)),
inference(superposition,[],[f1653,f1307]) ).
fof(f1307,plain,
! [X0,X1] : ld(X0,X1) = mult(X0,ld(X0,ld(X0,X1))),
inference(superposition,[],[f735,f20]) ).
fof(f735,plain,
! [X2,X0,X1] : mult(X1,ld(X1,X0)) = ld(ld(X1,X2),mult(ld(X1,X2),X0)),
inference(backward_demodulation,[],[f641,f725]) ).
fof(f725,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,X0),X1),
inference(backward_demodulation,[],[f624,f724]) ).
fof(f724,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(forward_demodulation,[],[f722,f434]) ).
fof(f434,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(ld(X0,X0),ld(X1,X1)),
inference(superposition,[],[f349,f57]) ).
fof(f722,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(mult(ld(X0,X0),ld(X1,X1)),X1),
inference(backward_demodulation,[],[f529,f715]) ).
fof(f715,plain,
! [X0,X1] : mult(X1,ld(X0,X0)) = rd(X1,ld(X0,X0)),
inference(forward_demodulation,[],[f708,f536]) ).
fof(f536,plain,
! [X0,X1] : mult(X1,ld(X0,X0)) = mult(rd(X1,ld(X0,X0)),ld(X0,X0)),
inference(superposition,[],[f531,f228]) ).
fof(f228,plain,
! [X0] : ld(X0,X0) = ld(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[],[f215,f58]) ).
fof(f58,plain,
! [X0] : ld(X0,X0) = mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))),
inference(forward_demodulation,[],[f46,f51]) ).
fof(f46,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(rd(X0,X0),rd(X0,X0)))),
inference(superposition,[],[f30,f37]) ).
fof(f215,plain,
! [X0] : ld(ld(X0,X0),ld(X0,X0)) = mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))),
inference(superposition,[],[f118,f35]) ).
fof(f118,plain,
! [X0,X1] : mult(ld(X0,X0),X1) = mult(X0,ld(X0,mult(ld(X0,X0),X1))),
inference(superposition,[],[f103,f35]) ).
fof(f531,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[],[f530,f501]) ).
fof(f530,plain,
! [X0,X1] : mult(mult(X0,ld(X1,X1)),X1) = mult(rd(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[],[f512,f228]) ).
fof(f512,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),X1) = mult(mult(X0,ld(ld(X1,X1),ld(X1,X1))),X1),
inference(superposition,[],[f501,f349]) ).
fof(f708,plain,
! [X0,X1] : rd(X1,ld(X0,X0)) = mult(rd(X1,ld(X0,X0)),ld(X0,X0)),
inference(superposition,[],[f677,f228]) ).
fof(f677,plain,
! [X0,X1] : rd(X0,X1) = mult(rd(X0,X1),ld(X1,X1)),
inference(superposition,[],[f302,f21]) ).
fof(f529,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(rd(ld(X0,X0),ld(X1,X1)),X1),
inference(forward_demodulation,[],[f528,f56]) ).
fof(f528,plain,
! [X0,X1] : mult(rd(ld(X0,X0),ld(X1,X1)),X1) = mult(X0,ld(X0,mult(ld(X1,X1),X1))),
inference(forward_demodulation,[],[f527,f103]) ).
fof(f527,plain,
! [X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(rd(ld(X0,X0),ld(X1,X1)),X1),
inference(forward_demodulation,[],[f511,f228]) ).
fof(f511,plain,
! [X0,X1] : mult(rd(ld(X0,X0),ld(X1,X1)),X1) = mult(mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))),X1),
inference(superposition,[],[f501,f57]) ).
fof(f624,plain,
! [X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X0),X1),
inference(superposition,[],[f501,f434]) ).
fof(f641,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = mult(ld(X1,X1),X0),
inference(backward_demodulation,[],[f97,f624]) ).
fof(f97,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,ld(X0,X0))),X0),
inference(superposition,[],[f31,f56]) ).
fof(f1653,plain,
! [X0,X1] : mult(X0,X1) = ld(ld(X0,X0),mult(X0,X1)),
inference(forward_demodulation,[],[f1631,f1629]) ).
fof(f1629,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,ld(ld(X0,X0),mult(X0,X1)))),
inference(superposition,[],[f169,f725]) ).
fof(f169,plain,
! [X0,X1] : mult(X0,X1) = mult(ld(X0,X0),ld(ld(X0,X0),mult(X0,X1))),
inference(forward_demodulation,[],[f167,f56]) ).
fof(f167,plain,
! [X0,X1] : mult(ld(X0,X0),ld(ld(X0,X0),mult(X0,X1))) = mult(mult(ld(X0,X0),X0),X1),
inference(superposition,[],[f103,f153]) ).
fof(f153,plain,
! [X0] : ld(ld(X0,X0),X0) = X0,
inference(backward_demodulation,[],[f54,f152]) ).
fof(f152,plain,
! [X0] : mult(ld(X0,X0),ld(ld(X0,X0),X0)) = X0,
inference(forward_demodulation,[],[f145,f56]) ).
fof(f145,plain,
! [X0] : mult(ld(X0,X0),ld(ld(X0,X0),X0)) = mult(ld(X0,X0),X0),
inference(superposition,[],[f135,f54]) ).
fof(f54,plain,
! [X0] : ld(ld(X0,X0),X0) = mult(ld(X0,X0),ld(ld(X0,X0),X0)),
inference(backward_demodulation,[],[f40,f51]) ).
fof(f40,plain,
! [X0] : ld(rd(X0,X0),X0) = mult(rd(X0,X0),ld(rd(X0,X0),X0)),
inference(superposition,[],[f22,f37]) ).
fof(f1631,plain,
! [X0,X1] : ld(ld(X0,X0),mult(X0,X1)) = mult(X0,ld(X0,ld(ld(X0,X0),mult(X0,X1)))),
inference(superposition,[],[f735,f169]) ).
fof(f2599,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = mult(X2,mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1))))),
inference(forward_demodulation,[],[f2525,f2564]) ).
fof(f2564,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(backward_demodulation,[],[f1379,f2563]) ).
fof(f2563,plain,
! [X2,X0,X1] : mult(X0,ld(X0,ld(X2,X2))) = mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X2,X2))),
inference(forward_demodulation,[],[f2562,f734]) ).
fof(f734,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(X0,ld(X0,X1)),X1),
inference(backward_demodulation,[],[f579,f725]) ).
fof(f579,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(ld(X0,X0),X1),X1),
inference(forward_demodulation,[],[f548,f448]) ).
fof(f448,plain,
! [X2,X0] : mult(X0,ld(X0,ld(X2,X2))) = mult(rd(ld(X0,X0),X0),mult(X0,ld(X2,X2))),
inference(backward_demodulation,[],[f360,f434]) ).
fof(f360,plain,
! [X2,X0] : mult(ld(X0,X0),ld(X2,X2)) = mult(rd(ld(X0,X0),X0),mult(X0,ld(X2,X2))),
inference(backward_demodulation,[],[f304,f349]) ).
fof(f304,plain,
! [X2,X0] : mult(rd(ld(X0,X0),X0),mult(rd(X0,X2),X2)) = mult(ld(X0,X0),ld(X2,X2)),
inference(backward_demodulation,[],[f279,f302]) ).
fof(f279,plain,
! [X2,X0,X1] : mult(rd(ld(X0,X0),X0),mult(rd(X0,X2),X2)) = rd(mult(ld(X0,X0),rd(X1,X2)),rd(X1,X2)),
inference(superposition,[],[f32,f55]) ).
fof(f55,plain,
! [X0] : ld(X0,X0) = mult(rd(ld(X0,X0),X0),X0),
inference(backward_demodulation,[],[f39,f51]) ).
fof(f548,plain,
! [X0,X1] : rd(mult(ld(X0,X0),X1),X1) = mult(rd(ld(X0,X0),X0),mult(X0,ld(X1,X1))),
inference(superposition,[],[f351,f55]) ).
fof(f351,plain,
! [X2,X0,X1] : rd(mult(mult(X1,X2),X0),X0) = mult(X1,mult(X2,ld(X0,X0))),
inference(backward_demodulation,[],[f292,f349]) ).
fof(f2562,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X2,X2))) = rd(mult(X0,ld(X0,X2)),X2),
inference(forward_demodulation,[],[f2513,f1314]) ).
fof(f1314,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))),
inference(backward_demodulation,[],[f142,f1313]) ).
fof(f1313,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(forward_demodulation,[],[f1293,f103]) ).
fof(f1293,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X1)),X2)),
inference(superposition,[],[f735,f22]) ).
fof(f142,plain,
! [X2,X0,X1] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(forward_demodulation,[],[f130,f103]) ).
fof(f130,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(superposition,[],[f22,f103]) ).
fof(f2513,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X2,X2))) = rd(mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))),X2),
inference(superposition,[],[f734,f103]) ).
fof(f1379,plain,
! [X0,X1] : ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))) = mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X1,X1))),
inference(superposition,[],[f22,f736]) ).
fof(f736,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = mult(mult(X1,ld(X1,X0)),ld(X0,X0)),
inference(backward_demodulation,[],[f642,f725]) ).
fof(f642,plain,
! [X0,X1] : mult(mult(X1,ld(X1,X0)),ld(X0,X0)) = mult(ld(X1,X1),X0),
inference(backward_demodulation,[],[f90,f641]) ).
fof(f90,plain,
! [X2,X0,X1] : mult(mult(X1,ld(X1,X0)),ld(X0,X0)) = ld(ld(X1,X2),mult(ld(X1,X2),X0)),
inference(superposition,[],[f31,f33]) ).
fof(f2525,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = mult(X2,ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1))))),
inference(superposition,[],[f691,f734]) ).
fof(f691,plain,
! [X2,X3,X1] : mult(X3,ld(rd(X1,X2),rd(X1,X2))) = mult(X3,ld(X2,X2)),
inference(forward_demodulation,[],[f672,f671]) ).
fof(f671,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = rd(mult(X2,mult(X0,ld(X1,X1))),mult(X0,ld(X1,X1))),
inference(superposition,[],[f302,f348]) ).
fof(f672,plain,
! [X2,X3,X0,X1] : mult(X3,ld(rd(X1,X2),rd(X1,X2))) = rd(mult(X3,mult(X0,ld(X2,X2))),mult(X0,ld(X2,X2))),
inference(superposition,[],[f302,f302]) ).
fof(f1250,plain,
! [X2,X0,X1] : mult(mult(X2,ld(X0,X0)),X1) = mult(mult(X2,mult(X0,ld(X0,ld(X1,X1)))),X1),
inference(forward_demodulation,[],[f1249,f610]) ).
fof(f610,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,ld(X2,X2))),X2),
inference(forward_demodulation,[],[f609,f33]) ).
fof(f609,plain,
! [X2,X0,X1] : mult(mult(X0,mult(X1,ld(X2,X2))),X2) = mult(mult(X0,X1),mult(X2,ld(X2,X2))),
inference(forward_demodulation,[],[f576,f388]) ).
fof(f576,plain,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X2),ld(X2,X2)) = mult(mult(X0,mult(X1,ld(X2,X2))),X2),
inference(superposition,[],[f349,f351]) ).
fof(f1249,plain,
! [X2,X0,X1] : mult(mult(X2,mult(ld(X0,X0),ld(X1,X1))),X1) = mult(mult(X2,mult(X0,ld(X0,ld(X1,X1)))),X1),
inference(forward_demodulation,[],[f1248,f715]) ).
fof(f1248,plain,
! [X2,X0,X1] : mult(mult(X2,rd(ld(X0,X0),ld(X1,X1))),X1) = mult(mult(X2,mult(X0,ld(X0,ld(X1,X1)))),X1),
inference(forward_demodulation,[],[f1213,f228]) ).
fof(f1213,plain,
! [X2,X0,X1] : mult(mult(X2,rd(ld(X0,X0),ld(X1,X1))),X1) = mult(mult(X2,mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1))))),X1),
inference(superposition,[],[f610,f57]) ).
fof(f9011,plain,
mult(sK0,sK2) != mult(mult(sK0,ld(sK1,sK1)),sK2),
inference(trivial_inequality_removal,[],[f9010]) ).
fof(f9010,plain,
( mult(sK0,sK2) != mult(sK0,sK2)
| mult(sK0,sK2) != mult(mult(sK0,ld(sK1,sK1)),sK2) ),
inference(backward_demodulation,[],[f369,f9008]) ).
fof(f9008,plain,
! [X2,X0,X1] : mult(X0,X2) = mult(X0,mult(X1,ld(X1,X2))),
inference(forward_demodulation,[],[f8909,f135]) ).
fof(f8909,plain,
! [X2,X0,X1] : mult(X0,mult(X1,ld(X1,X2))) = mult(X0,mult(X0,ld(X0,X2))),
inference(superposition,[],[f135,f8826]) ).
fof(f8826,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(X0,ld(X0,mult(X1,ld(X1,X2)))),
inference(forward_demodulation,[],[f8825,f2728]) ).
fof(f2728,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(mult(X0,ld(X0,ld(X1,X1))),X2),
inference(forward_demodulation,[],[f2727,f725]) ).
fof(f2727,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(ld(X0,X0),X2),
inference(forward_demodulation,[],[f2726,f2626]) ).
fof(f2726,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(mult(ld(X0,X0),ld(X1,X1)),X2),
inference(forward_demodulation,[],[f2725,f715]) ).
fof(f2725,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(rd(ld(X0,X0),ld(X1,X1)),X2),
inference(forward_demodulation,[],[f2657,f1746]) ).
fof(f2657,plain,
! [X2,X0,X1] : mult(rd(ld(X0,X0),ld(X1,X1)),X2) = mult(mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))),X2),
inference(superposition,[],[f2626,f57]) ).
fof(f8825,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(X0,ld(X0,mult(X1,ld(X1,X2)))),
inference(backward_demodulation,[],[f8814,f8823]) ).
fof(f8823,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f8822,f3568]) ).
fof(f3568,plain,
! [X2,X0,X1] : mult(X0,X1) = mult(rd(ld(X0,X0),X2),ld(rd(ld(X0,X0),X2),mult(X0,X1))),
inference(superposition,[],[f2629,f1655]) ).
fof(f1655,plain,
! [X0,X1] : mult(X0,X1) = mult(ld(X0,X0),mult(X0,X1)),
inference(backward_demodulation,[],[f169,f1653]) ).
fof(f2629,plain,
! [X2,X0,X1] : mult(X0,X2) = mult(rd(X0,X1),ld(rd(X0,X1),mult(X0,X2))),
inference(backward_demodulation,[],[f440,f2626]) ).
fof(f440,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X1,X1)),X2) = mult(rd(X0,X1),ld(rd(X0,X1),mult(mult(X0,ld(X1,X1)),X2))),
inference(superposition,[],[f136,f349]) ).
fof(f136,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(X0,ld(X0,mult(mult(X0,X1),X2))),
inference(backward_demodulation,[],[f116,f135]) ).
fof(f116,plain,
! [X2,X0,X1] : mult(X0,ld(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,mult(X0,ld(X0,X1))),X2),
inference(superposition,[],[f103,f22]) ).
fof(f8822,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),mult(X0,ld(X0,ld(X1,X1))))) = mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f8821,f1746]) ).
fof(f8821,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))))) = mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f8820,f2564]) ).
fof(f8820,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f8819,f2029]) ).
fof(f2029,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(X0,mult(ld(X0,X1),ld(X1,X1))),
inference(superposition,[],[f388,f736]) ).
fof(f8819,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = mult(rd(ld(X0,X0),X1),mult(X0,mult(ld(X0,X1),ld(X1,X1)))),
inference(forward_demodulation,[],[f8818,f409]) ).
fof(f409,plain,
! [X2,X0,X1] : mult(X0,ld(X0,mult(X1,ld(X2,X2)))) = mult(X0,mult(ld(X0,X1),ld(X2,X2))),
inference(backward_demodulation,[],[f376,f408]) ).
fof(f408,plain,
! [X2,X0,X1] : rd(mult(X0,ld(X0,mult(X1,X2))),X2) = mult(X0,mult(ld(X0,X1),ld(X2,X2))),
inference(forward_demodulation,[],[f334,f349]) ).
fof(f334,plain,
! [X2,X0,X1] : rd(mult(X0,ld(X0,mult(X1,X2))),X2) = mult(X0,mult(rd(ld(X0,X1),X2),X2)),
inference(superposition,[],[f292,f103]) ).
fof(f376,plain,
! [X2,X0,X1] : rd(mult(X0,ld(X0,mult(X1,X2))),X2) = mult(X0,ld(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[],[f365,f103]) ).
fof(f365,plain,
! [X2,X0,X1] : rd(mult(X0,ld(X0,mult(X1,X2))),X2) = mult(mult(X0,ld(X0,X1)),ld(X2,X2)),
inference(backward_demodulation,[],[f129,f349]) ).
fof(f129,plain,
! [X2,X0,X1] : mult(rd(mult(X0,ld(X0,X1)),X2),X2) = rd(mult(X0,ld(X0,mult(X1,X2))),X2),
inference(superposition,[],[f23,f103]) ).
fof(f8818,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,mult(X1,ld(X1,X1))))),
inference(forward_demodulation,[],[f8817,f103]) ).
fof(f8817,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = mult(rd(ld(X0,X0),X1),mult(mult(X0,ld(X0,X1)),ld(X1,X1))),
inference(forward_demodulation,[],[f8816,f388]) ).
fof(f8816,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = mult(mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),ld(X1,X1)),
inference(forward_demodulation,[],[f8676,f4285]) ).
fof(f4285,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = rd(X2,mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f4284,f2626]) ).
fof(f4284,plain,
! [X2,X0,X1] : rd(X2,mult(X0,ld(X0,ld(X1,X1)))) = mult(mult(X2,ld(X0,X0)),ld(X1,X1)),
inference(forward_demodulation,[],[f4283,f715]) ).
fof(f4283,plain,
! [X2,X0,X1] : rd(X2,mult(X0,ld(X0,ld(X1,X1)))) = mult(rd(X2,ld(X0,X0)),ld(X1,X1)),
inference(forward_demodulation,[],[f4282,f2626]) ).
fof(f4282,plain,
! [X2,X0,X1] : rd(X2,mult(X0,ld(X0,ld(X1,X1)))) = mult(mult(rd(X2,ld(X0,X0)),ld(X1,X1)),ld(X1,X1)),
inference(forward_demodulation,[],[f4281,f3020]) ).
fof(f3020,plain,
! [X2,X0,X1] : mult(rd(X0,X1),ld(X2,X2)) = rd(X0,mult(X1,ld(X2,X2))),
inference(forward_demodulation,[],[f3019,f2638]) ).
fof(f2638,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = mult(X2,mult(X0,ld(mult(X0,ld(X1,X1)),ld(X1,X1)))),
inference(backward_demodulation,[],[f2293,f2632]) ).
fof(f2632,plain,
! [X0,X1] : ld(mult(X0,ld(X1,X1)),mult(X0,ld(X1,X1))) = mult(X0,ld(mult(X0,ld(X1,X1)),ld(X1,X1))),
inference(backward_demodulation,[],[f2169,f2626]) ).
fof(f2169,plain,
! [X0,X1] : ld(mult(X0,ld(X1,X1)),mult(X0,ld(X1,X1))) = mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),ld(X1,X1))),
inference(forward_demodulation,[],[f2119,f1746]) ).
fof(f2119,plain,
! [X0,X1] : ld(mult(X0,ld(X1,X1)),mult(X0,ld(ld(X1,X1),ld(X1,X1)))) = mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),ld(X1,X1))),
inference(superposition,[],[f441,f715]) ).
fof(f441,plain,
! [X0,X1] : mult(rd(X0,X1),ld(rd(X0,X1),X1)) = ld(rd(X0,X1),mult(X0,ld(X1,X1))),
inference(superposition,[],[f22,f349]) ).
fof(f2293,plain,
! [X2,X0,X1] : mult(X2,ld(X1,X1)) = mult(X2,ld(mult(X0,ld(X1,X1)),mult(X0,ld(X1,X1)))),
inference(superposition,[],[f691,f348]) ).
fof(f3019,plain,
! [X2,X0,X1] : rd(X0,mult(X1,ld(X2,X2))) = mult(rd(X0,X1),mult(X1,ld(mult(X1,ld(X2,X2)),ld(X2,X2)))),
inference(forward_demodulation,[],[f3018,f2762]) ).
fof(f2762,plain,
! [X2,X0,X1] : ld(mult(X0,ld(X1,X1)),mult(X0,X2)) = mult(X0,ld(mult(X0,ld(X1,X1)),X2)),
inference(forward_demodulation,[],[f2687,f2626]) ).
fof(f2687,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),X2)) = ld(mult(X0,ld(X1,X1)),mult(X0,X2)),
inference(superposition,[],[f22,f2626]) ).
fof(f3018,plain,
! [X2,X0,X1] : rd(X0,mult(X1,ld(X2,X2))) = mult(rd(X0,X1),ld(mult(X1,ld(X2,X2)),mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[],[f2970,f2785]) ).
fof(f2785,plain,
! [X2,X0,X1] : rd(X0,X2) = rd(mult(X0,ld(X1,X1)),X2),
inference(forward_demodulation,[],[f2710,f695]) ).
fof(f695,plain,
! [X0,X1] : rd(X0,X1) = rd(mult(X0,ld(X1,X1)),X1),
inference(backward_demodulation,[],[f478,f677]) ).
fof(f478,plain,
! [X0,X1] : mult(rd(X0,X1),ld(X1,X1)) = rd(mult(X0,ld(X1,X1)),X1),
inference(superposition,[],[f348,f349]) ).
fof(f2710,plain,
! [X2,X0,X1] : rd(mult(X0,ld(X1,X1)),X2) = rd(mult(X0,ld(X2,X2)),X2),
inference(superposition,[],[f695,f2626]) ).
fof(f2970,plain,
! [X2,X0,X1] : mult(rd(X0,X1),ld(mult(X1,ld(X2,X2)),mult(X1,ld(X2,X2)))) = rd(mult(X0,ld(X2,X2)),mult(X1,ld(X2,X2))),
inference(superposition,[],[f348,f2601]) ).
fof(f2601,plain,
! [X2,X0,X1] : mult(X0,ld(X2,X2)) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(backward_demodulation,[],[f583,f2600]) ).
fof(f583,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,ld(X2,X2))) = mult(X0,mult(X1,ld(X1,ld(X2,X2)))),
inference(forward_demodulation,[],[f582,f434]) ).
fof(f582,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,ld(X2,X2))) = mult(X0,mult(ld(X1,X1),ld(X2,X2))),
inference(forward_demodulation,[],[f551,f351]) ).
fof(f551,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,ld(X2,X2))) = rd(mult(mult(X0,ld(X1,X1)),X2),X2),
inference(superposition,[],[f351,f349]) ).
fof(f4281,plain,
! [X2,X0,X1] : rd(X2,mult(X0,ld(X0,ld(X1,X1)))) = mult(rd(X2,mult(ld(X0,X0),ld(X1,X1))),ld(X1,X1)),
inference(forward_demodulation,[],[f4280,f715]) ).
fof(f4280,plain,
! [X2,X0,X1] : rd(X2,mult(X0,ld(X0,ld(X1,X1)))) = mult(rd(X2,rd(ld(X0,X0),ld(X1,X1))),ld(X1,X1)),
inference(forward_demodulation,[],[f4215,f1746]) ).
fof(f4215,plain,
! [X2,X0,X1] : mult(rd(X2,rd(ld(X0,X0),ld(X1,X1))),ld(X1,X1)) = rd(X2,mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1))))),
inference(superposition,[],[f3020,f57]) ).
fof(f8676,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = rd(mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),mult(X0,ld(X0,ld(X1,X1)))),
inference(superposition,[],[f734,f6839]) ).
fof(f6839,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(rd(ld(X0,X0),X1),mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f6838,f1868]) ).
fof(f1868,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(ld(X0,X0),X1),
inference(forward_demodulation,[],[f1842,f1325]) ).
fof(f1325,plain,
! [X3,X0,X1] : mult(X0,ld(X0,X3)) = mult(ld(X0,X1),ld(ld(X0,X1),X3)),
inference(forward_demodulation,[],[f1324,f1313]) ).
fof(f1324,plain,
! [X2,X3,X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X3)) = ld(mult(X0,ld(X0,X2)),mult(X0,ld(X0,mult(X2,X3)))),
inference(forward_demodulation,[],[f1294,f103]) ).
fof(f1294,plain,
! [X2,X3,X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X3)) = ld(mult(X0,ld(X0,X2)),mult(mult(X0,ld(X0,X2)),X3)),
inference(superposition,[],[f735,f735]) ).
fof(f1842,plain,
! [X0,X1] : ld(ld(X0,X0),X1) = mult(ld(X0,X0),ld(ld(X0,X0),X1)),
inference(superposition,[],[f1689,f1746]) ).
fof(f1689,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(X0,X0),ld(X0,X1)),
inference(superposition,[],[f1655,f1307]) ).
fof(f6838,plain,
! [X0,X1] : ld(rd(ld(X0,X0),X1),mult(X0,ld(X0,ld(X1,X1)))) = ld(ld(X0,X0),X1),
inference(forward_demodulation,[],[f6820,f4699]) ).
fof(f4699,plain,
! [X2,X0,X1] : ld(ld(X0,X1),X2) = mult(ld(X0,X0),ld(ld(X0,X1),X2)),
inference(forward_demodulation,[],[f4698,f3257]) ).
fof(f3257,plain,
! [X2,X0,X1] : ld(ld(X0,X1),X2) = mult(X0,ld(X0,ld(ld(X0,X1),X2))),
inference(superposition,[],[f1325,f1307]) ).
fof(f4698,plain,
! [X2,X0,X1] : ld(ld(X0,X1),X2) = mult(ld(X0,X0),mult(X0,ld(X0,ld(ld(X0,X1),X2)))),
inference(forward_demodulation,[],[f4646,f1868]) ).
fof(f4646,plain,
! [X2,X0,X1] : ld(ld(X0,X1),X2) = mult(ld(X0,X0),ld(ld(X0,X0),ld(ld(X0,X1),X2))),
inference(superposition,[],[f1355,f1689]) ).
fof(f1355,plain,
! [X2,X0,X1] : ld(mult(X0,X1),X2) = mult(X0,ld(X0,ld(mult(X0,X1),X2))),
inference(superposition,[],[f136,f1307]) ).
fof(f6820,plain,
! [X0,X1] : ld(rd(ld(X0,X0),X1),mult(X0,ld(X0,ld(X1,X1)))) = mult(ld(X0,X0),ld(ld(X0,X0),X1)),
inference(backward_demodulation,[],[f62,f6803]) ).
fof(f6803,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(rd(X0,X1),ld(rd(X0,X1),X2)),
inference(forward_demodulation,[],[f6802,f1868]) ).
fof(f6802,plain,
! [X2,X0,X1] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = ld(ld(X0,X0),X2),
inference(forward_demodulation,[],[f6767,f4699]) ).
fof(f6767,plain,
! [X2,X0,X1] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(ld(X0,X0),ld(ld(X0,X0),X2)),
inference(superposition,[],[f1325,f6097]) ).
fof(f6097,plain,
! [X0,X1] : rd(X0,X1) = ld(ld(X0,X0),rd(X0,X1)),
inference(superposition,[],[f5807,f3569]) ).
fof(f3569,plain,
! [X0,X1] : mult(rd(X0,X1),ld(rd(X0,X1),X0)) = X0,
inference(superposition,[],[f2629,f33]) ).
fof(f5807,plain,
! [X0,X1] : ld(ld(mult(X0,X1),mult(X0,X1)),X0) = X0,
inference(superposition,[],[f5694,f1355]) ).
fof(f5694,plain,
! [X0,X1] : ld(mult(X0,ld(X0,ld(X1,X1))),X0) = X0,
inference(backward_demodulation,[],[f3739,f5687]) ).
fof(f5687,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,ld(mult(X0,ld(X1,X1)),ld(X1,X1))),
inference(backward_demodulation,[],[f2759,f5678]) ).
fof(f5678,plain,
! [X2,X0,X1] : mult(X0,ld(X0,ld(X2,X2))) = ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[],[f5677,f5676]) ).
fof(f5676,plain,
! [X2,X3,X0,X1,X4] : mult(X0,ld(X0,ld(X4,X4))) = mult(mult(X0,X1),mult(ld(mult(X0,mult(X1,ld(X2,X2))),ld(X3,X3)),ld(X4,X4))),
inference(forward_demodulation,[],[f5520,f3291]) ).
fof(f3291,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(mult(X0,X1),ld(mult(X0,X1),X2)),
inference(forward_demodulation,[],[f3245,f1325]) ).
fof(f3245,plain,
! [X2,X0,X1] : mult(mult(X0,X1),ld(mult(X0,X1),X2)) = mult(ld(X0,X0),ld(ld(X0,X0),X2)),
inference(superposition,[],[f1325,f1653]) ).
fof(f5520,plain,
! [X2,X3,X0,X1,X4] : mult(mult(X0,mult(X1,ld(X2,X2))),ld(mult(X0,mult(X1,ld(X2,X2))),ld(X4,X4))) = mult(mult(X0,X1),mult(ld(mult(X0,mult(X1,ld(X2,X2))),ld(X3,X3)),ld(X4,X4))),
inference(superposition,[],[f2652,f2625]) ).
fof(f2625,plain,
! [X3,X0,X1] : mult(X0,mult(ld(X0,ld(X1,X1)),ld(X3,X3))) = mult(X0,ld(X0,ld(X3,X3))),
inference(forward_demodulation,[],[f2624,f725]) ).
fof(f2624,plain,
! [X3,X0,X1] : mult(X0,mult(ld(X0,ld(X1,X1)),ld(X3,X3))) = mult(ld(X0,X0),ld(X3,X3)),
inference(backward_demodulation,[],[f372,f2601]) ).
fof(f372,plain,
! [X3,X0,X1] : mult(rd(ld(X0,X0),X1),mult(X1,ld(X3,X3))) = mult(X0,mult(ld(X0,ld(X1,X1)),ld(X3,X3))),
inference(forward_demodulation,[],[f356,f349]) ).
fof(f356,plain,
! [X3,X0,X1] : mult(X0,mult(rd(ld(X0,ld(X1,X1)),X3),X3)) = mult(rd(ld(X0,X0),X1),mult(X1,ld(X3,X3))),
inference(backward_demodulation,[],[f298,f349]) ).
fof(f298,plain,
! [X3,X0,X1] : mult(rd(ld(X0,X0),X1),mult(rd(X1,X3),X3)) = mult(X0,mult(rd(ld(X0,ld(X1,X1)),X3),X3)),
inference(forward_demodulation,[],[f281,f32]) ).
fof(f281,plain,
! [X2,X3,X0,X1] : mult(rd(ld(X0,X0),X1),mult(rd(X1,X3),X3)) = rd(mult(mult(X0,ld(X0,ld(X1,X1))),rd(X2,X3)),rd(X2,X3)),
inference(superposition,[],[f32,f57]) ).
fof(f2652,plain,
! [X2,X3,X0,X1] : mult(mult(X0,mult(X1,ld(X2,X2))),X3) = mult(mult(X0,X1),X3),
inference(superposition,[],[f2626,f388]) ).
fof(f5677,plain,
! [X2,X0,X1] : ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2)))) = mult(mult(X0,X1),mult(ld(mult(X0,mult(X1,ld(X2,X2))),ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2))))),ld(X2,X2))),
inference(forward_demodulation,[],[f5521,f2297]) ).
fof(f2297,plain,
! [X2,X3,X0,X1] : mult(X3,ld(X2,X2)) = mult(X3,ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2))))),
inference(superposition,[],[f691,f351]) ).
fof(f5521,plain,
! [X2,X0,X1] : ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2)))) = mult(mult(X0,X1),mult(ld(mult(X0,mult(X1,ld(X2,X2))),ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2))))),ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2)))))),
inference(superposition,[],[f2652,f1084]) ).
fof(f1084,plain,
! [X0] : ld(X0,X0) = mult(X0,mult(ld(X0,ld(X0,X0)),ld(X0,X0))),
inference(forward_demodulation,[],[f1053,f228]) ).
fof(f1053,plain,
! [X0] : ld(X0,X0) = mult(X0,mult(ld(X0,ld(X0,X0)),ld(ld(X0,X0),ld(X0,X0)))),
inference(superposition,[],[f420,f35]) ).
fof(f420,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X1,ld(mult(X0,X1),mult(X0,X1)))),
inference(forward_demodulation,[],[f342,f349]) ).
fof(f342,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(rd(X1,mult(X0,X1)),mult(X0,X1))),
inference(superposition,[],[f292,f21]) ).
fof(f2759,plain,
! [X0,X1] : mult(X0,ld(mult(X0,ld(X1,X1)),ld(X1,X1))) = ld(mult(X0,mult(X0,ld(X1,X1))),mult(X0,mult(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f2682,f2632]) ).
fof(f2682,plain,
! [X0,X1] : ld(mult(X0,ld(X1,X1)),mult(X0,ld(X1,X1))) = ld(mult(X0,mult(X0,ld(X1,X1))),mult(X0,mult(X0,ld(X1,X1)))),
inference(superposition,[],[f2151,f2626]) ).
fof(f2151,plain,
! [X0] : ld(X0,X0) = ld(mult(X0,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f2150,f1307]) ).
fof(f2150,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = ld(mult(X0,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f2149,f1746]) ).
fof(f2149,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(mult(X0,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f2148,f471]) ).
fof(f471,plain,
! [X0] : mult(mult(X0,X0),ld(mult(X0,X0),ld(X0,X0))) = ld(mult(X0,X0),mult(X0,X0)),
inference(superposition,[],[f22,f429]) ).
fof(f429,plain,
! [X0] : mult(X0,X0) = mult(mult(X0,X0),ld(X0,X0)),
inference(superposition,[],[f349,f21]) ).
fof(f2148,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = mult(mult(X0,X0),ld(mult(X0,X0),ld(X0,X0))),
inference(forward_demodulation,[],[f2110,f1775]) ).
fof(f1775,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = ld(mult(X0,X1),mult(mult(X0,X1),X2)),
inference(forward_demodulation,[],[f1754,f1325]) ).
fof(f1754,plain,
! [X2,X0,X1] : mult(ld(X0,X0),ld(ld(X0,X0),X2)) = ld(mult(X0,X1),mult(mult(X0,X1),X2)),
inference(superposition,[],[f735,f1653]) ).
fof(f2110,plain,
! [X0] : mult(mult(X0,X0),ld(mult(X0,X0),ld(X0,X0))) = ld(mult(X0,X0),mult(mult(X0,X0),ld(ld(X0,X0),ld(X0,X0)))),
inference(superposition,[],[f441,f499]) ).
fof(f499,plain,
! [X0] : mult(X0,X0) = rd(mult(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[],[f498,f135]) ).
fof(f498,plain,
! [X0] : mult(X0,mult(X0,ld(X0,X0))) = rd(mult(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[],[f497,f388]) ).
fof(f497,plain,
! [X0] : mult(mult(X0,X0),ld(X0,X0)) = rd(mult(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[],[f487,f228]) ).
fof(f487,plain,
! [X0] : mult(mult(X0,X0),ld(ld(X0,X0),ld(X0,X0))) = rd(mult(X0,X0),ld(X0,X0)),
inference(superposition,[],[f348,f429]) ).
fof(f3739,plain,
! [X0,X1] : ld(mult(X0,ld(mult(X0,ld(X1,X1)),ld(X1,X1))),X0) = X0,
inference(forward_demodulation,[],[f3716,f2762]) ).
fof(f3716,plain,
! [X0,X1] : ld(ld(mult(X0,ld(X1,X1)),mult(X0,ld(X1,X1))),X0) = X0,
inference(superposition,[],[f3687,f715]) ).
fof(f3687,plain,
! [X0,X1] : ld(ld(rd(X0,X1),rd(X0,X1)),X0) = X0,
inference(superposition,[],[f1653,f3569]) ).
fof(f62,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),X1)) = ld(rd(ld(X0,X0),X1),mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f50,f51]) ).
fof(f50,plain,
! [X0,X1] : mult(rd(rd(X0,X0),X1),ld(rd(rd(X0,X0),X1),X1)) = ld(rd(rd(X0,X0),X1),mult(X0,ld(X0,ld(X1,X1)))),
inference(superposition,[],[f22,f30]) ).
fof(f8814,plain,
! [X2,X0,X1] : mult(X0,ld(X0,mult(X1,ld(X1,X2)))) = mult(mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),X2),
inference(forward_demodulation,[],[f8813,f725]) ).
fof(f8813,plain,
! [X2,X0,X1] : mult(X0,ld(X0,mult(ld(X1,X1),X2))) = mult(mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),X2),
inference(forward_demodulation,[],[f8812,f103]) ).
fof(f8812,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),X2),
inference(forward_demodulation,[],[f8674,f4796]) ).
fof(f4796,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X2) = mult(rd(ld(X0,X0),X3),ld(rd(ld(X0,X0),X3),mult(mult(X0,X1),X2))),
inference(superposition,[],[f2629,f1688]) ).
fof(f1688,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(ld(X0,X0),mult(mult(X0,X1),X2)),
inference(superposition,[],[f1655,f136]) ).
fof(f8674,plain,
! [X2,X0,X1] : mult(rd(ld(X0,X0),X1),ld(rd(ld(X0,X0),X1),mult(mult(X0,ld(X0,ld(X1,X1))),X2))) = mult(mult(rd(ld(X0,X0),X1),mult(X0,ld(X0,X1))),X2),
inference(superposition,[],[f103,f6839]) ).
fof(f369,plain,
( mult(sK0,sK2) != mult(sK0,mult(sK1,ld(sK1,sK2)))
| mult(sK0,sK2) != mult(mult(sK0,ld(sK1,sK1)),sK2) ),
inference(backward_demodulation,[],[f28,f349]) ).
fof(f28,plain,
( mult(sK0,sK2) != mult(sK0,mult(sK1,ld(sK1,sK2)))
| mult(sK0,sK2) != mult(mult(rd(sK0,sK1),sK1),sK2) ),
inference(backward_demodulation,[],[f27,f23]) ).
fof(f27,plain,
( mult(sK0,sK2) != mult(sK0,mult(sK1,ld(sK1,sK2)))
| mult(sK0,sK2) != mult(rd(mult(sK0,sK1),sK1),sK2) ),
inference(backward_demodulation,[],[f19,f22]) ).
fof(f19,plain,
( mult(sK0,sK2) != mult(rd(mult(sK0,sK1),sK1),sK2)
| mult(sK0,sK2) != mult(sK0,ld(sK1,mult(sK1,sK2))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( mult(sK0,sK2) != mult(rd(mult(sK0,sK1),sK1),sK2)
| mult(sK0,sK2) != mult(sK0,ld(sK1,mult(sK1,sK2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).
fof(f17,plain,
( ? [X0,X1,X2] :
( mult(X0,X2) != mult(rd(mult(X0,X1),X1),X2)
| mult(X0,X2) != mult(X0,ld(X1,mult(X1,X2))) )
=> ( mult(sK0,sK2) != mult(rd(mult(sK0,sK1),sK1),sK2)
| mult(sK0,sK2) != mult(sK0,ld(sK1,mult(sK1,sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] :
( mult(X0,X2) != mult(rd(mult(X0,X1),X1),X2)
| mult(X0,X2) != mult(X0,ld(X1,mult(X1,X2))) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
~ ! [X0,X1,X2] :
( mult(X0,X2) = mult(rd(mult(X0,X1),X1),X2)
& mult(X0,X2) = mult(X0,ld(X1,mult(X1,X2))) ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X4,X5,X6] :
( mult(X4,X6) = mult(rd(mult(X4,X5),X5),X6)
& mult(X4,ld(X5,mult(X5,X6))) = mult(X4,X6) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X4,X5,X6] :
( mult(X4,X6) = mult(rd(mult(X4,X5),X5),X6)
& mult(X4,ld(X5,mult(X5,X6))) = mult(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri May 3 20:39:07 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.10/0.29 % (27035)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.30 % (27038)WARNING: value z3 for option sas not known
% 0.10/0.30 % (27040)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.31 % (27038)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.31 % (27041)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.31 % (27037)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.31 % (27042)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.31 % (27036)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.31 % (27039)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.31 TRYING [1]
% 0.14/0.31 TRYING [2]
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 TRYING [3]
% 0.14/0.33 TRYING [3]
% 0.14/0.33 TRYING [4]
% 0.14/0.37 TRYING [4]
% 0.14/0.39 TRYING [5]
% 0.14/0.47 TRYING [1]
% 0.14/0.47 TRYING [2]
% 0.14/0.47 TRYING [3]
% 0.14/0.48 TRYING [4]
% 0.14/0.50 % (27041)First to succeed.
% 0.14/0.51 % (27041)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27035"
% 0.14/0.51 % (27041)Refutation found. Thanks to Tanya!
% 0.14/0.51 % SZS status Theorem for theBenchmark
% 0.14/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.51 % (27041)------------------------------
% 0.14/0.51 % (27041)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.51 % (27041)Termination reason: Refutation
% 0.14/0.51
% 0.14/0.51 % (27041)Memory used [KB]: 3978
% 0.14/0.51 % (27041)Time elapsed: 0.201 s
% 0.14/0.51 % (27041)Instructions burned: 562 (million)
% 0.14/0.51 % (27035)Success in time 0.214 s
%------------------------------------------------------------------------------