TSTP Solution File: RNG006-10 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG006-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:32:34 EDT 2023
% Result : Unsatisfiable 172.80s 22.11s
% Output : CNFRefutation 175.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 161 (; 161 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : sum(additive_identity,X,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : sum(X,Y,add(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,Z,W,Y,V,X] : ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,Z,V,X,W,U] : ifeq(sum(Y,Z,V),true,ifeq(sum(X,V,W),true,ifeq(sum(X,Y,U),true,sum(U,Z,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,V3,V4,Z,V2,Y,V1] : ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,V,U] : ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,V,U] : ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
sum(b,additive_inverse(c),bS_Ic) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(a,b,aPb) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(a,c,aPc) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
product(a,bS_Ic,aPb_S_IaPc) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f26,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f27,plain,
! [X0] : sum(additive_identity,X0,X0) = true,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f28,plain,
! [X0] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f30,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f31,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity) = true,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X0,X5),true,sum(X5,X1,X4),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f35,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f42,plain,
! [X0,X1,X2,X3] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f44,plain,
sum(b,additive_inverse(c),bS_Ic) = true,
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f45,plain,
product(a,b,aPb) = true,
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f46,plain,
product(a,c,aPc) = true,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f47,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f48,plain,
product(a,bS_Ic,aPb_S_IaPc) != true,
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(true,true,ifeq(sum(X5,X3,X1),true,sum(multiply(X0,X5),X4,X2),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f29,f38]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X5,X3,X1),true,sum(multiply(X0,X5),X4,X2),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f142]) ).
fof(f296,plain,
ifeq(true,true,sum(additive_inverse(c),b,bS_Ic),true) = true,
inference(paramodulation,[status(thm)],[f44,f35]) ).
fof(f297,plain,
sum(additive_inverse(c),b,bS_Ic) = true,
inference(forward_demodulation,[status(thm)],[f26,f296]) ).
fof(f302,plain,
! [X0,X1] : ifeq(true,true,sum(X0,X1,add(X1,X0)),true) = true,
inference(paramodulation,[status(thm)],[f30,f35]) ).
fof(f303,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)) = true,
inference(forward_demodulation,[status(thm)],[f26,f302]) ).
fof(f390,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f27,f33]) ).
fof(f391,plain,
! [X0,X1,X2,X3] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f390]) ).
fof(f473,plain,
! [X0,X1,X2,X3,X4] : ifeq(true,true,ifeq(sum(X0,add(X1,X2),X3),true,ifeq(sum(X0,X1,X4),true,sum(X4,X2,X3),true),true),true) = true,
inference(paramodulation,[status(thm)],[f30,f34]) ).
fof(f474,plain,
! [X0,X1,X2,X3,X4] : ifeq(sum(X0,add(X1,X2),X3),true,ifeq(sum(X0,X1,X4),true,sum(X4,X2,X3),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f473]) ).
fof(f534,plain,
! [X0] : ifeq2(true,true,ifeq2(sum(aPb,additive_inverse(aPc),X0),true,X0,aPb_S_IaPc),aPb_S_IaPc) = aPb_S_IaPc,
inference(paramodulation,[status(thm)],[f47,f42]) ).
fof(f535,plain,
! [X0] : ifeq2(sum(aPb,additive_inverse(aPc),X0),true,X0,aPb_S_IaPc) = aPb_S_IaPc,
inference(forward_demodulation,[status(thm)],[f25,f534]) ).
fof(f546,plain,
! [X0] : ifeq2(sum(additive_inverse(c),b,X0),true,ifeq2(true,true,bS_Ic,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f297,f42]) ).
fof(f547,plain,
! [X0] : ifeq2(sum(additive_inverse(c),b,X0),true,bS_Ic,X0) = X0,
inference(forward_demodulation,[status(thm)],[f25,f546]) ).
fof(f560,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f28,f42]) ).
fof(f561,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,X0,X1) = X1,
inference(forward_demodulation,[status(thm)],[f25,f560]) ).
fof(f567,plain,
ifeq2(true,true,bS_Ic,add(b,additive_inverse(c))) = add(b,additive_inverse(c)),
inference(paramodulation,[status(thm)],[f303,f547]) ).
fof(f568,plain,
bS_Ic = add(b,additive_inverse(c)),
inference(forward_demodulation,[status(thm)],[f25,f567]) ).
fof(f772,plain,
! [X0] : ifeq2(product(a,c,X0),true,ifeq2(true,true,aPc,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f46,f43]) ).
fof(f773,plain,
! [X0] : ifeq2(product(a,c,X0),true,aPc,X0) = X0,
inference(forward_demodulation,[status(thm)],[f25,f772]) ).
fof(f779,plain,
ifeq2(true,true,aPc,multiply(a,c)) = multiply(a,c),
inference(paramodulation,[status(thm)],[f29,f773]) ).
fof(f780,plain,
aPc = multiply(a,c),
inference(forward_demodulation,[status(thm)],[f25,f779]) ).
fof(f3102,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X2,X0,b),true,sum(multiply(a,X2),X1,aPb),true),true),true) = true,
inference(paramodulation,[status(thm)],[f45,f143]) ).
fof(f3103,plain,
! [X0,X1,X2] : ifeq(product(a,X0,X1),true,ifeq(sum(X2,X0,b),true,sum(multiply(a,X2),X1,aPb),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f3102]) ).
fof(f8399,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,ifeq(true,true,sum(additive_inverse(X0),X2,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f31,f391]) ).
fof(f8400,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(additive_inverse(X0),X2,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f8399]) ).
fof(f9149,plain,
! [X0] : ifeq(true,true,sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),true) = true,
inference(paramodulation,[status(thm)],[f31,f8400]) ).
fof(f9150,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0) = true,
inference(forward_demodulation,[status(thm)],[f26,f9149]) ).
fof(f9162,plain,
! [X0,X1] : ifeq(true,true,sum(additive_inverse(X0),add(X1,X0),X1),true) = true,
inference(paramodulation,[status(thm)],[f303,f8400]) ).
fof(f9163,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1) = true,
inference(forward_demodulation,[status(thm)],[f26,f9162]) ).
fof(f9220,plain,
! [X0] : ifeq2(true,true,additive_inverse(additive_inverse(X0)),X0) = X0,
inference(paramodulation,[status(thm)],[f9150,f561]) ).
fof(f9221,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f25,f9220]) ).
fof(f9794,plain,
! [X0,X1] : sum(X0,add(X1,additive_inverse(X0)),X1) = true,
inference(paramodulation,[status(thm)],[f9221,f9163]) ).
fof(f9805,plain,
sum(additive_inverse(additive_inverse(c)),bS_Ic,b) = true,
inference(paramodulation,[status(thm)],[f568,f9163]) ).
fof(f9806,plain,
sum(c,bS_Ic,b) = true,
inference(forward_demodulation,[status(thm)],[f9221,f9805]) ).
fof(f24798,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(sum(X0,X1,X2),true,sum(X2,additive_inverse(X0),X1),true),true) = true,
inference(paramodulation,[status(thm)],[f9794,f474]) ).
fof(f24799,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X2,additive_inverse(X0),X1),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f24798]) ).
fof(f252455,plain,
! [X0] : ifeq(product(a,bS_Ic,X0),true,ifeq(true,true,sum(multiply(a,c),X0,aPb),true),true) = true,
inference(paramodulation,[status(thm)],[f9806,f3103]) ).
fof(f252456,plain,
! [X0] : ifeq(product(a,bS_Ic,X0),true,sum(multiply(a,c),X0,aPb),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f252455]) ).
fof(f252457,plain,
! [X0] : ifeq(product(a,bS_Ic,X0),true,sum(aPc,X0,aPb),true) = true,
inference(forward_demodulation,[status(thm)],[f780,f252456]) ).
fof(f252492,plain,
ifeq(true,true,sum(aPc,multiply(a,bS_Ic),aPb),true) = true,
inference(paramodulation,[status(thm)],[f29,f252457]) ).
fof(f252493,plain,
sum(aPc,multiply(a,bS_Ic),aPb) = true,
inference(forward_demodulation,[status(thm)],[f26,f252492]) ).
fof(f252818,plain,
ifeq(true,true,sum(aPb,additive_inverse(aPc),multiply(a,bS_Ic)),true) = true,
inference(paramodulation,[status(thm)],[f252493,f24799]) ).
fof(f252819,plain,
sum(aPb,additive_inverse(aPc),multiply(a,bS_Ic)) = true,
inference(forward_demodulation,[status(thm)],[f26,f252818]) ).
fof(f254702,plain,
ifeq2(true,true,multiply(a,bS_Ic),aPb_S_IaPc) = aPb_S_IaPc,
inference(paramodulation,[status(thm)],[f252819,f535]) ).
fof(f254703,plain,
multiply(a,bS_Ic) = aPb_S_IaPc,
inference(forward_demodulation,[status(thm)],[f25,f254702]) ).
fof(f255929,plain,
product(a,bS_Ic,aPb_S_IaPc) = true,
inference(paramodulation,[status(thm)],[f254703,f29]) ).
fof(f255930,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f255929,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : RNG006-10 : TPTP v8.1.2. Released v7.3.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:38:23 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 172.80/22.11 % Refutation found
% 172.80/22.11 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 172.80/22.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 181.00/23.64 % Elapsed time: 23.070555 seconds
% 181.00/23.64 % CPU time: 154.768435 seconds
% 181.00/23.64 % Memory used: 1.784 GB
%------------------------------------------------------------------------------