%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:06:17 PM UTC 2026
% Result : Unsatisfiable 3.28s 0.89s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 135 ( 135 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : sum(X,Y,add(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : ifeq(product(X,Y,Z),true,product(Y,X,Z),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : product(X,multiplicative_identity,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [V1,V2,V4,Y,Z,V3,X] : ifeq(product(V1,V2,V4),true,ifeq(product(Y,Z,V3),true,ifeq(sum(X,Z,V2),true,ifeq(sum(X,Y,V1),true,sum(X,V3,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : sum(X,inverse(X),multiplicative_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product(inverse(X),X,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y,V,U] : ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Y,V,U] : ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
sum(x,x,x) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [X0] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0] : product(X0,multiplicative_identity,X0) = true,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X6,X4,X1),true,ifeq(sum(X6,X3,X0),true,sum(X6,X5,X2),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0] : sum(X0,inverse(X0),multiplicative_identity) = true,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
! [X0] : product(inverse(X0),X0,additive_identity) = true,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f48,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(thm)],[f23]) ).
fof(f49,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(thm)],[f24]) ).
fof(f50,plain,
sum(x,x,x) != true,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f64,plain,
! [X0,X1] : ifeq(true,true,sum(X0,X1,add(X1,X0)),true) = true,
inference(paramodulation,[status(thm)],[f28,f30]) ).
fof(f66,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)) = true,
inference(forward_demodulation,[status(thm)],[f27,f64]) ).
fof(f90,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f33,f48]) ).
fof(f91,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X1,X0),X2),X2) = X2,
inference(paramodulation,[status(thm)],[f66,f48]) ).
fof(f102,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,X0,X1) = X1,
inference(forward_demodulation,[status(thm)],[f26,f90]) ).
fof(f103,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,add(X1,X0),X2) = X2,
inference(forward_demodulation,[status(thm)],[f26,f91]) ).
fof(f107,plain,
! [X0] : ifeq2(true,true,add(inverse(X0),X0),multiplicative_identity) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f45,f103]) ).
fof(f114,plain,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
inference(forward_demodulation,[status(thm)],[f26,f107]) ).
fof(f331,plain,
! [X0,X1] : ifeq(true,true,product(X0,X1,multiply(X1,X0)),true) = true,
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f341,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)) = true,
inference(forward_demodulation,[status(thm)],[f27,f331]) ).
fof(f421,plain,
! [X0,X1] : ifeq2(product(inverse(X0),X0,X1),true,ifeq2(true,true,additive_identity,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f46,f49]) ).
fof(f433,plain,
! [X0,X1] : ifeq2(product(inverse(X0),X0,X1),true,additive_identity,X1) = X1,
inference(forward_demodulation,[status(thm)],[f26,f421]) ).
fof(f1071,plain,
! [X0] : ifeq2(true,true,additive_identity,multiply(inverse(X0),X0)) = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f29,f433]) ).
fof(f1077,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f1071]) ).
fof(f1405,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,add(X1,X2),X3),true,ifeq(product(X4,X1,X5),true,ifeq(true,true,ifeq(sum(X2,X4,X0),true,sum(X2,X5,X3),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f66,f41]) ).
fof(f1436,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,add(X1,X2),X3),true,ifeq(product(X4,X1,X5),true,ifeq(sum(X2,X4,X0),true,sum(X2,X5,X3),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f1405]) ).
fof(f1458,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,add(X1,X2),X3),true,ifeq(true,true,ifeq(sum(X2,X4,X0),true,sum(X2,multiply(X1,X4),X3),true),true),true) = true,
inference(paramodulation,[status(thm)],[f341,f1436]) ).
fof(f1482,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,add(X1,X2),X3),true,ifeq(sum(X2,X4,X0),true,sum(X2,multiply(X1,X4),X3),true),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f1458]) ).
fof(f1668,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,multiplicative_identity,X1),true,ifeq(sum(X2,X3,X0),true,sum(X2,multiply(inverse(X2),X3),X1),true),true) = true,
inference(paramodulation,[status(thm)],[f114,f1482]) ).
fof(f1739,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(sum(X0,X1,X2),true,sum(X0,multiply(inverse(X0),X1),X2),true),true) = true,
inference(paramodulation,[status(thm)],[f35,f1668]) ).
fof(f1766,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X0,multiply(inverse(X0),X1),X2),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f1739]) ).
fof(f1791,plain,
! [X0,X1] : ifeq(sum(X0,X0,X1),true,sum(X0,additive_identity,X1),true) = true,
inference(paramodulation,[status(thm)],[f1077,f1766]) ).
fof(f2101,plain,
! [X0] : ifeq(true,true,sum(X0,additive_identity,add(X0,X0)),true) = true,
inference(paramodulation,[status(thm)],[f66,f1791]) ).
fof(f2121,plain,
! [X0] : sum(X0,additive_identity,add(X0,X0)) = true,
inference(forward_demodulation,[status(thm)],[f27,f2101]) ).
fof(f2149,plain,
! [X0] : ifeq2(true,true,X0,add(X0,X0)) = add(X0,X0),
inference(paramodulation,[status(thm)],[f2121,f102]) ).
fof(f2211,plain,
! [X0] : X0 = add(X0,X0),
inference(forward_demodulation,[status(thm)],[f26,f2149]) ).
fof(f2307,plain,
! [X0] : sum(X0,X0,X0) = true,
inference(paramodulation,[status(thm)],[f2211,f66]) ).
fof(f2313,plain,
true != true,
inference(backward_demodulation,[status(thm)],[f2307,f50]) ).
fof(f2315,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:48:33 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 3.28/0.89 % Refutation found
% 3.28/0.89 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.28/0.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/0.92 % Elapsed time: 0.546401 seconds
% 0.39/0.92 % CPU time: 4.141660 seconds
% 0.39/0.92 % Total memory used: 136.639 MB
% 0.39/0.92 % Net memory used: 134.807 MB
%------------------------------------------------------------------------------