TSTP Solution File: GRP777+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Wed May 31 12:12:40 EDT 2023
% Result : Theorem 99.77s 12.97s
% Output : CNFRefutation 100.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 10
% Syntax : Number of formulae : 173 ( 173 unt; 0 def)
% Number of atoms : 173 ( 172 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 365 (; 364 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : difference(A,product(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : product(A,difference(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : quotient(product(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : product(quotient(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [D,C,B,A] : product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : product(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A] : product(product(product(A,B),B),product(B,product(B,A))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [C,B,A] : bigC(A,B,C) = product(product(A,B),product(C,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [X0] : bigC(a,b,X0) = bigC(c,c,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [X0] : bigC(a,b,X0) = bigC(c,c,X0),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f13,plain,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f15,plain,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : product(product(X0,X1),product(X2,X3)) = product(product(X0,X2),product(X1,X3)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f17,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f18,plain,
! [X0,X1] : product(product(product(X0,X1),X1),product(X1,product(X1,X0))) = X1,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = product(product(X0,X1),product(X2,X0)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f20,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f21,plain,
? [X0] : bigC(a,b,X0) != bigC(c,c,X0),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f22,plain,
bigC(a,b,sk0_0) != bigC(c,c,sk0_0),
inference(skolemization,[status(esa)],[f21]) ).
fof(f23,plain,
bigC(a,b,sk0_0) != bigC(c,c,sk0_0),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : bigC(product(X0,X1),X2,product(X1,X3)) = product(product(product(X0,X1),X2),bigC(X1,X3,X0)),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f1051,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X0,X1),product(X1,X2)) = product(product(X0,X1),bigC(X1,X2,X0)),
inference(paramodulation,[status(thm)],[f17,f25]) ).
fof(f1108,plain,
! [X0,X1] : bigC(X0,X1,X0) = product(product(X0,X1),X0),
inference(paramodulation,[status(thm)],[f17,f19]) ).
fof(f1109,plain,
! [X0,X1] : bigC(X0,X0,X1) = product(X0,product(X1,X0)),
inference(paramodulation,[status(thm)],[f17,f19]) ).
fof(f1225,plain,
! [X0,X1,X2] : difference(product(X0,X1),bigC(X0,X1,X2)) = product(X2,X0),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f1245,plain,
quotient(product(a,b),product(c,b)) = product(a,c),
inference(paramodulation,[status(thm)],[f20,f14]) ).
fof(f1246,plain,
! [X0,X1,X2] : quotient(bigC(X0,X1,X2),product(X2,X0)) = product(X0,X1),
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f1261,plain,
! [X0,X1] : quotient(X0,difference(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f13,f14]) ).
fof(f1307,plain,
! [X0,X1,X2] : bigC(difference(X0,X1),X2,X0) = product(product(difference(X0,X1),X2),X1),
inference(paramodulation,[status(thm)],[f13,f19]) ).
fof(f1308,plain,
! [X0,X1,X2] : bigC(X0,difference(X0,X1),X2) = product(X1,product(X2,X0)),
inference(paramodulation,[status(thm)],[f13,f19]) ).
fof(f1340,plain,
! [X0,X1] : difference(quotient(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f1386,plain,
! [X0,X1,X2] : bigC(X0,X1,quotient(X2,X0)) = product(product(X0,X1),X2),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f1387,plain,
! [X0,X1,X2] : bigC(quotient(X0,X1),X1,X2) = product(X0,product(X2,quotient(X0,X1))),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f1448,plain,
! [X0,X1] : quotient(bigC(X0,X1,X0),X0) = product(X0,X1),
inference(paramodulation,[status(thm)],[f1108,f14]) ).
fof(f1752,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = product(product(X0,X2),product(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f16]) ).
fof(f1753,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = bigC(X0,X2,X1),
inference(forward_demodulation,[status(thm)],[f19,f1752]) ).
fof(f1756,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X0,X1),X2) = product(product(X0,X2),product(X1,product(X0,X1))),
inference(paramodulation,[status(thm)],[f1109,f16]) ).
fof(f1757,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X0,X1),X2) = product(product(X0,X2),bigC(X1,X1,X0)),
inference(forward_demodulation,[status(thm)],[f1109,f1756]) ).
fof(f1774,plain,
! [X0,X1,X2,X3,X4,X5] : product(product(product(X0,X1),product(X2,X3)),product(X4,X5)) = product(product(product(X0,X2),X4),product(product(X1,X3),X5)),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f1776,plain,
! [X0,X1,X2,X3,X4] : product(bigC(X0,X1,X2),product(X3,X4)) = product(product(product(X0,X1),X3),product(product(X2,X0),X4)),
inference(paramodulation,[status(thm)],[f19,f16]) ).
fof(f1778,plain,
! [X0,X1,X2,X3] : product(bigC(X0,X0,X1),product(X2,X3)) = product(product(X0,X2),product(product(X1,X0),X3)),
inference(paramodulation,[status(thm)],[f1109,f16]) ).
fof(f1779,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,X2)) = product(product(X3,X1),product(difference(X3,X0),X2)),
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f1780,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(product(X0,X1),product(X0,X2)),
inference(paramodulation,[status(thm)],[f17,f16]) ).
fof(f1877,plain,
! [X0,X1,X2,X3] : bigC(product(X0,X1),product(X0,X1),product(X2,X3)) = product(product(X0,X1),product(product(X2,X0),product(X3,X1))),
inference(paramodulation,[status(thm)],[f16,f1109]) ).
fof(f1878,plain,
! [X0,X1,X2,X3] : product(product(X0,product(X1,X2)),bigC(X3,X3,X0)) = product(product(X0,X3),product(product(X1,X0),product(X2,X3))),
inference(forward_demodulation,[status(thm)],[f1757,f1877]) ).
fof(f1879,plain,
! [X0,X1,X2,X3] : product(product(X0,product(X1,X2)),bigC(X3,X3,X0)) = product(bigC(X0,X0,X1),product(X3,product(X2,X3))),
inference(forward_demodulation,[status(thm)],[f1778,f1878]) ).
fof(f1880,plain,
! [X0,X1,X2,X3] : product(product(X0,product(X1,X2)),bigC(X3,X3,X0)) = product(bigC(X0,X0,X1),bigC(X3,X3,X2)),
inference(forward_demodulation,[status(thm)],[f1109,f1879]) ).
fof(f1910,plain,
! [X0,X1,X2,X3,X4] : bigC(product(X0,X1),X2,product(X3,X4)) = product(product(product(X0,X1),X2),product(product(X3,X0),product(X4,X1))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f1911,plain,
! [X0,X1,X2,X3,X4] : bigC(product(X0,X1),X2,product(X3,X4)) = product(bigC(X0,X1,X3),product(X2,product(X4,X1))),
inference(forward_demodulation,[status(thm)],[f1776,f1910]) ).
fof(f2041,plain,
! [X0,X1,X2] : product(product(X0,product(X1,X2)),bigC(X1,X1,X0)) = product(product(X0,X1),bigC(X1,X2,X0)),
inference(backward_demodulation,[status(thm)],[f1757,f1051]) ).
fof(f2042,plain,
! [X0,X1,X2] : product(bigC(X0,X0,X1),bigC(X1,X1,X2)) = product(product(X0,X1),bigC(X1,X2,X0)),
inference(forward_demodulation,[status(thm)],[f1880,f2041]) ).
fof(f2085,plain,
! [X0,X1] : product(product(X0,X1),product(X1,product(X1,quotient(X0,X1)))) = X1,
inference(paramodulation,[status(thm)],[f15,f18]) ).
fof(f2099,plain,
product(product(product(a,b),product(c,b)),product(product(c,b),product(product(c,b),product(a,c)))) = product(c,b),
inference(paramodulation,[status(thm)],[f20,f18]) ).
fof(f2100,plain,
product(product(product(a,c),product(c,b)),product(product(b,b),product(product(c,b),product(a,c)))) = product(c,b),
inference(forward_demodulation,[status(thm)],[f1774,f2099]) ).
fof(f2101,plain,
product(product(a,b),product(product(b,b),product(product(c,b),product(a,c)))) = product(c,b),
inference(forward_demodulation,[status(thm)],[f20,f2100]) ).
fof(f2102,plain,
product(product(a,b),product(bigC(b,b,c),product(b,product(a,c)))) = product(c,b),
inference(forward_demodulation,[status(thm)],[f1778,f2101]) ).
fof(f2103,plain,
product(product(a,b),product(bigC(b,c,b),product(b,product(a,c)))) = product(c,b),
inference(forward_demodulation,[status(thm)],[f1753,f2102]) ).
fof(f2104,plain,
product(product(a,b),bigC(product(b,c),b,product(b,a))) = product(c,b),
inference(forward_demodulation,[status(thm)],[f1911,f2103]) ).
fof(f2334,plain,
! [X0,X1] : quotient(bigC(X0,X0,X1),X0) = product(X0,X1),
inference(paramodulation,[status(thm)],[f1753,f1448]) ).
fof(f2451,plain,
! [X0,X1] : difference(product(X0,X1),bigC(X0,X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f2334,f1340]) ).
fof(f2501,plain,
! [X0,X1] : difference(X0,bigC(X1,X1,difference(X1,X0))) = X1,
inference(paramodulation,[status(thm)],[f13,f2451]) ).
fof(f2586,plain,
! [X0,X1] : product(X0,X1) = bigC(X1,X1,difference(X1,X0)),
inference(paramodulation,[status(thm)],[f2501,f13]) ).
fof(f2652,plain,
! [X0,X1] : difference(product(X0,X0),product(X1,X0)) = product(difference(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2586,f1225]) ).
fof(f2653,plain,
! [X0,X1] : difference(X0,product(X1,X0)) = product(difference(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f17,f2652]) ).
fof(f2690,plain,
! [X0,X1] : difference(X0,X1) = product(difference(X0,quotient(X1,X0)),X0),
inference(paramodulation,[status(thm)],[f15,f2653]) ).
fof(f2759,plain,
! [X0,X1] : quotient(difference(X0,X1),X0) = difference(X0,quotient(X1,X0)),
inference(paramodulation,[status(thm)],[f2690,f14]) ).
fof(f2836,plain,
! [X0,X1,X2] : quotient(product(X0,X1),product(X1,X2)) = difference(product(X1,X2),quotient(bigC(X1,X2,X0),product(X1,X2))),
inference(paramodulation,[status(thm)],[f1225,f2759]) ).
fof(f2846,plain,
! [X0,X1] : quotient(X0,X1) = difference(X1,quotient(product(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f12,f2759]) ).
fof(f2895,plain,
! [X0,X1] : product(X0,quotient(X1,X0)) = quotient(product(X0,X1),X0),
inference(paramodulation,[status(thm)],[f2846,f13]) ).
fof(f3975,plain,
! [X0,X1,X2] : bigC(X0,quotient(X1,X0),X2) = product(product(X0,X2),X1),
inference(paramodulation,[status(thm)],[f1753,f1386]) ).
fof(f3984,plain,
! [X0,X1,X2] : bigC(X0,X1,product(X0,quotient(X2,X0))) = product(product(X0,X1),product(X0,X2)),
inference(paramodulation,[status(thm)],[f2895,f1386]) ).
fof(f3985,plain,
! [X0,X1,X2] : bigC(X0,X1,product(X0,quotient(X2,X0))) = product(X0,product(X1,X2)),
inference(forward_demodulation,[status(thm)],[f1780,f3984]) ).
fof(f4118,plain,
! [X0,X1,X2] : bigC(X0,X1,difference(X0,X2)) = product(X2,product(X1,X0)),
inference(paramodulation,[status(thm)],[f1753,f1308]) ).
fof(f4194,plain,
! [X0,X1,X2] : product(X0,product(difference(X1,X2),X1)) = product(X2,product(difference(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f1308,f4118]) ).
fof(f4267,plain,
! [X0,X1] : product(difference(X0,X1),product(X0,product(X0,quotient(difference(X0,quotient(X1,X0)),X0)))) = X0,
inference(paramodulation,[status(thm)],[f2690,f2085]) ).
fof(f4268,plain,
! [X0,X1] : product(difference(X0,X1),product(X0,product(X0,difference(X0,quotient(quotient(X1,X0),X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f2759,f4267]) ).
fof(f4269,plain,
! [X0,X1] : product(difference(X0,X1),product(X0,quotient(quotient(X1,X0),X0))) = X0,
inference(forward_demodulation,[status(thm)],[f13,f4268]) ).
fof(f4442,plain,
! [X0,X1] : bigC(product(X0,X1),product(X1,product(X1,quotient(X0,X1))),product(X0,X1)) = product(X1,product(X0,X1)),
inference(paramodulation,[status(thm)],[f2085,f1108]) ).
fof(f4443,plain,
! [X0,X1] : bigC(product(X0,X1),product(X0,X1),product(X1,product(X1,quotient(X0,X1)))) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1753,f4442]) ).
fof(f4444,plain,
! [X0,X1] : product(product(X0,product(X1,product(X1,quotient(X0,X1)))),bigC(X1,X1,X0)) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1757,f4443]) ).
fof(f4445,plain,
! [X0,X1] : product(bigC(X0,X0,X1),bigC(X1,X1,product(X1,quotient(X0,X1)))) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1880,f4444]) ).
fof(f4446,plain,
! [X0,X1] : product(product(X0,X1),bigC(X1,product(X1,quotient(X0,X1)),X0)) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f2042,f4445]) ).
fof(f4447,plain,
! [X0,X1] : product(product(X0,X1),bigC(X1,X0,product(X1,quotient(X0,X1)))) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1753,f4446]) ).
fof(f4448,plain,
! [X0,X1] : product(product(X0,X1),product(X1,product(X0,X0))) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f3985,f4447]) ).
fof(f4449,plain,
! [X0,X1] : product(product(X0,X1),product(X1,X0)) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f17,f4448]) ).
fof(f4450,plain,
! [X0,X1] : bigC(X0,X1,X1) = product(X1,product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f4449]) ).
fof(f4451,plain,
! [X0,X1] : bigC(X0,X1,X1) = bigC(X1,X1,X0),
inference(forward_demodulation,[status(thm)],[f1109,f4450]) ).
fof(f4454,plain,
! [X0,X1] : difference(product(X0,X1),X1) = product(X1,product(X1,quotient(X0,X1))),
inference(paramodulation,[status(thm)],[f2085,f12]) ).
fof(f4647,plain,
! [X0,X1] : bigC(X0,X1,X1) = bigC(X1,X0,X1),
inference(paramodulation,[status(thm)],[f1753,f4451]) ).
fof(f4701,plain,
! [X0,X1] : quotient(bigC(X0,X0,X1),product(X0,X1)) = product(X1,X0),
inference(paramodulation,[status(thm)],[f4451,f1246]) ).
fof(f4934,plain,
! [X0,X1] : difference(product(X0,X1),bigC(X1,X0,X0)) = product(X0,X0),
inference(paramodulation,[status(thm)],[f4647,f1225]) ).
fof(f4935,plain,
! [X0,X1] : difference(product(X0,X1),bigC(X1,X0,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f17,f4934]) ).
fof(f5157,plain,
! [X0,X1] : bigC(X0,difference(X0,X1),difference(X0,X1)) = product(product(difference(X0,X1),difference(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f4451,f1307]) ).
fof(f5158,plain,
! [X0,X1] : product(X0,product(difference(X1,X0),X1)) = product(product(difference(X1,X0),difference(X1,X0)),X0),
inference(forward_demodulation,[status(thm)],[f1308,f5157]) ).
fof(f5159,plain,
! [X0,X1] : product(X0,product(difference(X1,X0),X1)) = product(difference(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f17,f5158]) ).
fof(f5175,plain,
! [X0,X1] : bigC(difference(X0,quotient(X1,X0)),X0,X0) = product(difference(X0,X1),quotient(X1,X0)),
inference(paramodulation,[status(thm)],[f2690,f1307]) ).
fof(f5176,plain,
! [X0,X1] : bigC(X0,difference(X0,quotient(X1,X0)),X0) = product(difference(X0,X1),quotient(X1,X0)),
inference(forward_demodulation,[status(thm)],[f4647,f5175]) ).
fof(f5177,plain,
! [X0,X1] : product(quotient(X0,X1),product(X1,X1)) = product(difference(X1,X0),quotient(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1308,f5176]) ).
fof(f5178,plain,
! [X0,X1] : product(quotient(X0,X1),X1) = product(difference(X1,X0),quotient(X0,X1)),
inference(forward_demodulation,[status(thm)],[f17,f5177]) ).
fof(f5179,plain,
! [X0,X1] : X0 = product(difference(X1,X0),quotient(X0,X1)),
inference(forward_demodulation,[status(thm)],[f15,f5178]) ).
fof(f5228,plain,
! [X0,X1] : difference(product(X0,difference(X0,X1)),product(product(difference(X0,X1),X0),X1)) = X0,
inference(paramodulation,[status(thm)],[f1307,f4935]) ).
fof(f5229,plain,
! [X0,X1] : difference(X0,product(product(difference(X1,X0),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f13,f5228]) ).
fof(f5230,plain,
! [X0,X1] : product(difference(X0,product(difference(X1,X0),X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f2653,f5229]) ).
fof(f5846,plain,
! [X0,X1] : difference(difference(X0,X1),X1) = quotient(X1,X0),
inference(paramodulation,[status(thm)],[f5179,f12]) ).
fof(f5966,plain,
! [X0,X1] : difference(X0,product(X1,X0)) = quotient(product(X1,X0),X1),
inference(paramodulation,[status(thm)],[f12,f5846]) ).
fof(f5967,plain,
! [X0,X1] : product(difference(X0,X1),X0) = quotient(product(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f2653,f5966]) ).
fof(f5968,plain,
! [X0,X1] : product(difference(X0,X1),X0) = product(X1,quotient(X0,X1)),
inference(forward_demodulation,[status(thm)],[f2895,f5967]) ).
fof(f6657,plain,
! [X0,X1] : quotient(X0,X1) = difference(X1,product(difference(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f5230,f14]) ).
fof(f6848,plain,
! [X0,X1] : difference(quotient(X0,X1),product(difference(X0,X1),X0)) = quotient(product(difference(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f6657,f5846]) ).
fof(f6863,plain,
! [X0,X1] : quotient(product(difference(X0,X1),X0),quotient(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f6657,f1261]) ).
fof(f6954,plain,
! [X0,X1] : difference(quotient(X0,X1),product(difference(X0,X1),X0)) = product(difference(quotient(X0,X1),X1),quotient(X0,X1)),
inference(paramodulation,[status(thm)],[f6863,f2690]) ).
fof(f6955,plain,
! [X0,X1] : quotient(product(difference(X0,X1),X0),X1) = product(difference(quotient(X0,X1),X1),quotient(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6848,f6954]) ).
fof(f6956,plain,
! [X0,X1] : quotient(product(difference(X0,X1),X0),X1) = product(X1,quotient(quotient(X0,X1),X1)),
inference(forward_demodulation,[status(thm)],[f5968,f6955]) ).
fof(f7062,plain,
! [X0,X1] : quotient(product(X0,quotient(X1,X0)),X1) = difference(X1,X0),
inference(paramodulation,[status(thm)],[f5968,f14]) ).
fof(f7246,plain,
quotient(product(product(c,b),product(a,c)),product(a,b)) = difference(product(a,b),product(c,b)),
inference(paramodulation,[status(thm)],[f1245,f7062]) ).
fof(f7247,plain,
quotient(product(product(c,a),product(b,c)),product(a,b)) = difference(product(a,b),product(c,b)),
inference(forward_demodulation,[status(thm)],[f16,f7246]) ).
fof(f7248,plain,
quotient(bigC(c,a,b),product(a,b)) = difference(product(a,b),product(c,b)),
inference(forward_demodulation,[status(thm)],[f19,f7247]) ).
fof(f7258,plain,
! [X0,X1] : quotient(product(difference(X0,X1),X0),X1) = difference(X1,difference(X0,X1)),
inference(paramodulation,[status(thm)],[f1261,f7062]) ).
fof(f7294,plain,
! [X0,X1] : difference(X0,difference(X1,X0)) = product(X0,quotient(quotient(X1,X0),X0)),
inference(backward_demodulation,[status(thm)],[f7258,f6956]) ).
fof(f7303,plain,
! [X0,X1] : product(difference(X0,X1),difference(X0,difference(X1,X0))) = X0,
inference(backward_demodulation,[status(thm)],[f7294,f4269]) ).
fof(f7501,plain,
! [X0,X1] : difference(difference(X0,X1),X0) = difference(X0,difference(X1,X0)),
inference(paramodulation,[status(thm)],[f7303,f12]) ).
fof(f7798,plain,
! [X0,X1] : difference(X0,X1) = difference(X1,difference(product(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f12,f7501]) ).
fof(f8087,plain,
! [X0,X1,X2,X3,X4,X5] : product(bigC(X0,X1,X2),product(X3,product(X4,X5))) = product(product(product(X0,X1),X3),product(product(X2,X4),product(X0,X5))),
inference(paramodulation,[status(thm)],[f16,f1776]) ).
fof(f8089,plain,
! [X0,X1,X2,X3,X4] : product(bigC(X0,X1,X2),product(X3,product(X4,X2))) = product(product(product(X0,X1),X3),bigC(X2,X0,X4)),
inference(paramodulation,[status(thm)],[f19,f1776]) ).
fof(f8096,plain,
! [X0,X1,X2,X3] : product(bigC(X0,X1,X2),product(X3,product(X2,X0))) = product(product(product(X0,X1),X3),product(X2,X0)),
inference(paramodulation,[status(thm)],[f17,f1776]) ).
fof(f8789,plain,
! [X0,X1] : product(X0,difference(X1,X0)) = difference(product(X0,X1),X0),
inference(paramodulation,[status(thm)],[f7798,f13]) ).
fof(f9358,plain,
! [X0,X1] : product(product(X0,difference(X1,X0)),product(X0,X1)) = product(X0,quotient(product(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f8789,f5968]) ).
fof(f9359,plain,
! [X0,X1] : product(product(X0,X0),product(difference(X1,X0),X1)) = product(X0,quotient(product(X0,X1),X0)),
inference(forward_demodulation,[status(thm)],[f16,f9358]) ).
fof(f9360,plain,
! [X0,X1] : product(X0,product(difference(X1,product(X0,X0)),X1)) = product(X0,quotient(product(X0,X1),X0)),
inference(forward_demodulation,[status(thm)],[f4194,f9359]) ).
fof(f9361,plain,
! [X0,X1] : product(X0,product(difference(X1,X0),X1)) = product(X0,quotient(product(X0,X1),X0)),
inference(forward_demodulation,[status(thm)],[f17,f9360]) ).
fof(f9362,plain,
! [X0,X1] : product(difference(X0,X1),X1) = product(X1,quotient(product(X1,X0),X1)),
inference(forward_demodulation,[status(thm)],[f5159,f9361]) ).
fof(f9363,plain,
! [X0,X1] : product(difference(X0,X1),X1) = product(X1,product(X1,quotient(X0,X1))),
inference(forward_demodulation,[status(thm)],[f2895,f9362]) ).
fof(f9364,plain,
! [X0,X1] : product(difference(X0,X1),X1) = difference(product(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f4454,f9363]) ).
fof(f10771,plain,
! [X0,X1,X2] : bigC(quotient(bigC(X0,X0,X1),product(X0,X1)),product(X0,X1),X2) = product(bigC(X0,X0,X1),product(X2,product(X1,X0))),
inference(paramodulation,[status(thm)],[f4701,f1387]) ).
fof(f10772,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X1,X0),X2) = product(bigC(X1,X1,X0),product(X2,product(X0,X1))),
inference(forward_demodulation,[status(thm)],[f4701,f10771]) ).
fof(f10773,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X1,X0),X2) = product(product(product(X1,X1),X2),product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f8096,f10772]) ).
fof(f10774,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X1,X0),X2) = product(product(X1,X2),product(X0,X1)),
inference(forward_demodulation,[status(thm)],[f17,f10773]) ).
fof(f10775,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X1,X0),X2) = bigC(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f19,f10774]) ).
fof(f10776,plain,
! [X0,X1,X2] : bigC(product(X0,X1),product(X1,X0),X2) = product(product(product(X0,X1),X2),bigC(X0,X0,X1)),
inference(paramodulation,[status(thm)],[f4701,f3975]) ).
fof(f10777,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = product(product(product(X2,X0),X1),bigC(X2,X2,X0)),
inference(forward_demodulation,[status(thm)],[f10775,f10776]) ).
fof(f11099,plain,
! [X0,X1,X2,X3,X4] : bigC(product(X0,X1),product(X2,X3),X4) = product(product(product(X0,X2),X4),product(product(X1,X3),product(X0,X1))),
inference(paramodulation,[status(thm)],[f19,f1774]) ).
fof(f11100,plain,
! [X0,X1,X2,X3,X4] : bigC(product(X0,X1),product(X2,X3),X4) = product(bigC(X0,X2,X1),product(X4,product(X3,X1))),
inference(forward_demodulation,[status(thm)],[f8087,f11099]) ).
fof(f11814,plain,
! [X0,X1,X2,X3,X4] : bigC(product(X0,X1),product(X2,X3),X4) = product(product(product(X0,X2),X4),bigC(X1,X0,X3)),
inference(backward_demodulation,[status(thm)],[f11100,f8089]) ).
fof(f11857,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = bigC(product(X2,X2),product(X0,X0),X1),
inference(backward_demodulation,[status(thm)],[f11814,f10777]) ).
fof(f11858,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = bigC(X2,product(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f17,f11857]) ).
fof(f11859,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = bigC(X2,X0,X1),
inference(forward_demodulation,[status(thm)],[f17,f11858]) ).
fof(f12842,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = bigC(X1,X0,X2),
inference(paramodulation,[status(thm)],[f1753,f11859]) ).
fof(f12852,plain,
! [X0,X1,X2] : bigC(X0,X1,X2) = bigC(X2,X1,X0),
inference(paramodulation,[status(thm)],[f1753,f11859]) ).
fof(f12887,plain,
! [X0,X1,X2] : quotient(bigC(X0,X1,X2),product(X0,X1)) = product(X1,X2),
inference(paramodulation,[status(thm)],[f11859,f1246]) ).
fof(f12928,plain,
! [X0,X1,X2] : quotient(bigC(X0,X1,X2),product(X1,X2)) = product(X2,X0),
inference(paramodulation,[status(thm)],[f11859,f1246]) ).
fof(f13059,plain,
! [X0,X1,X2] : quotient(product(X0,X1),product(X1,X2)) = difference(product(X1,X2),product(X2,X0)),
inference(backward_demodulation,[status(thm)],[f12887,f2836]) ).
fof(f13068,plain,
product(b,c) = difference(product(a,b),product(c,b)),
inference(backward_demodulation,[status(thm)],[f12928,f7248]) ).
fof(f33654,plain,
quotient(product(c,b),bigC(product(b,c),b,product(b,a))) = product(a,b),
inference(paramodulation,[status(thm)],[f2104,f14]) ).
fof(f33655,plain,
quotient(product(c,b),bigC(product(b,a),b,product(b,c))) = product(a,b),
inference(forward_demodulation,[status(thm)],[f12852,f33654]) ).
fof(f33656,plain,
quotient(product(c,b),bigC(b,product(b,a),product(b,c))) = product(a,b),
inference(forward_demodulation,[status(thm)],[f12842,f33655]) ).
fof(f33657,plain,
difference(product(a,b),product(c,b)) = bigC(product(b,c),b,product(b,a)),
inference(paramodulation,[status(thm)],[f2104,f12]) ).
fof(f33658,plain,
product(b,c) = bigC(product(b,c),b,product(b,a)),
inference(forward_demodulation,[status(thm)],[f13068,f33657]) ).
fof(f33659,plain,
product(b,c) = bigC(product(b,a),b,product(b,c)),
inference(forward_demodulation,[status(thm)],[f12852,f33658]) ).
fof(f33660,plain,
product(b,c) = bigC(b,product(b,a),product(b,c)),
inference(forward_demodulation,[status(thm)],[f12842,f33659]) ).
fof(f33736,plain,
quotient(product(c,b),product(b,c)) = product(a,b),
inference(backward_demodulation,[status(thm)],[f33660,f33656]) ).
fof(f33737,plain,
difference(product(b,c),product(c,c)) = product(a,b),
inference(forward_demodulation,[status(thm)],[f13059,f33736]) ).
fof(f33738,plain,
difference(product(b,c),c) = product(a,b),
inference(forward_demodulation,[status(thm)],[f17,f33737]) ).
fof(f33739,plain,
product(difference(b,c),c) = product(a,b),
inference(forward_demodulation,[status(thm)],[f9364,f33738]) ).
fof(f37317,plain,
! [X0] : product(c,product(X0,c)) = product(product(b,X0),product(a,b)),
inference(paramodulation,[status(thm)],[f33739,f1779]) ).
fof(f37318,plain,
! [X0] : bigC(c,c,X0) = product(product(b,X0),product(a,b)),
inference(forward_demodulation,[status(thm)],[f1109,f37317]) ).
fof(f37319,plain,
! [X0] : bigC(c,c,X0) = bigC(b,X0,a),
inference(forward_demodulation,[status(thm)],[f19,f37318]) ).
fof(f37320,plain,
! [X0] : bigC(c,c,X0) = bigC(a,X0,b),
inference(forward_demodulation,[status(thm)],[f12852,f37319]) ).
fof(f37483,plain,
bigC(a,b,sk0_0) != bigC(a,sk0_0,b),
inference(backward_demodulation,[status(thm)],[f37320,f23]) ).
fof(f37484,plain,
bigC(a,b,sk0_0) != bigC(a,b,sk0_0),
inference(forward_demodulation,[status(thm)],[f1753,f37483]) ).
fof(f37485,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f37484]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n019.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 11:28:25 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 99.77/12.97 % Refutation found
% 99.77/12.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 99.77/12.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 101.32/13.18 % Elapsed time: 12.853612 seconds
% 101.32/13.18 % CPU time: 101.037677 seconds
% 101.32/13.18 % Memory used: 799.254 MB
%------------------------------------------------------------------------------