%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:22:23 PM UTC 2026
% Result : Unsatisfiable 10.61s 1.85s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 15:35:27 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 10.61/1.85 % Refutation found
% 10.61/1.85 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.61/1.85 % SZS output start CNFRefutation for theBenchmark
% 10.61/1.85 fof(f1,axiom,(
% 10.61/1.85 (![X,V,W,Y,U,Z]: (( sum(X,V,W)| ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f2,axiom,(
% 10.61/1.85 (![U,Z,W,X,Y,V]: (( sum(U,Z,W)| ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(X,V,W) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f3,axiom,(
% 10.61/1.85 (![X]: (( sum(additive_identity,X,X)| ~ defined(X) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f4,axiom,(
% 10.61/1.85 (![X]: (( sum(additive_inverse(X),X,additive_identity)| ~ defined(X) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f5,axiom,(
% 10.61/1.85 (![Y,X,Z]: (( sum(Y,X,Z)| ~ sum(X,Y,Z) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f6,axiom,(
% 10.61/1.85 (![X,V,W,Y,U,Z]: (( product(X,V,W)| ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f7,axiom,(
% 10.61/1.85 (![U,Z,W,X,Y,V]: (( product(U,Z,W)| ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(X,V,W) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f8,axiom,(
% 10.61/1.85 (![X]: (( product(multiplicative_identity,X,X)| ~ defined(X) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f9,axiom,(
% 10.61/1.85 (![X]: (( product(multiplicative_inverse(X),X,multiplicative_identity)| sum(additive_identity,X,additive_identity)| ~ defined(X) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f10,axiom,(
% 10.61/1.85 (![Y,X,Z]: (( product(Y,X,Z)| ~ product(X,Y,Z) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f11,axiom,(
% 10.61/1.85 (![C,D,B,X,Y,A,Z]: (( sum(C,D,B)| ~ sum(X,Y,A)| ~ product(A,Z,B)| ~ product(X,Z,C)| ~ product(Y,Z,D) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.85 fof(f12,axiom,(
% 10.61/1.85 (![A,Z,B,X,Y,C,D]: (( product(A,Z,B)| ~ sum(X,Y,A)| ~ product(X,Z,C)| ~ product(Y,Z,D)| ~ sum(C,D,B) ) ))),
% 10.61/1.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f14,axiom,(
% 10.61/1.86 defined(additive_identity) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f15,axiom,(
% 10.61/1.86 (![X]: (( defined(additive_inverse(X))| ~ defined(X) ) ))),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f17,axiom,(
% 10.61/1.86 defined(multiplicative_identity) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f23,axiom,(
% 10.61/1.86 (![X,Y]: (( less_or_equal(X,Y)| less_or_equal(Y,X)| ~ defined(X)| ~ defined(Y) ) ))),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f26,axiom,(
% 10.61/1.86 ~ sum(additive_identity,additive_identity,multiplicative_identity) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f27,hypothesis,(
% 10.61/1.86 defined(a) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f28,hypothesis,(
% 10.61/1.86 defined(b) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f29,hypothesis,(
% 10.61/1.86 defined(c) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f30,negated_conjecture,(
% 10.61/1.86 ~ sum(additive_identity,a,additive_identity) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f31,negated_conjecture,(
% 10.61/1.86 ~ sum(additive_identity,b,additive_identity) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f32,negated_conjecture,(
% 10.61/1.86 product(a,b,c) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f33,negated_conjecture,(
% 10.61/1.86 sum(additive_identity,c,additive_identity) ),
% 10.61/1.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.61/1.86 fof(f34,plain,(
% 10.61/1.86 ![W,U,Z]: ((![V,Y]: ((![X]: (sum(X,V,W)|~sum(X,Y,U)))|~sum(Y,Z,V)))|~sum(U,Z,W))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f1])).
% 10.61/1.86 fof(f35,plain,(
% 10.61/1.86 ![X0,X1,X2,X3,X4,X5]: (sum(X0,X1,X2)|~sum(X0,X3,X4)|~sum(X3,X5,X1)|~sum(X4,X5,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f34])).
% 10.61/1.86 fof(f36,plain,(
% 10.61/1.86 ![W,X,V]: ((![Z,Y]: ((![U]: (sum(U,Z,W)|~sum(X,Y,U)))|~sum(Y,Z,V)))|~sum(X,V,W))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f2])).
% 10.61/1.86 fof(f37,plain,(
% 10.61/1.86 ![X0,X1,X2,X3,X4,X5]: (sum(X0,X1,X2)|~sum(X3,X4,X0)|~sum(X4,X1,X5)|~sum(X3,X5,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f36])).
% 10.61/1.86 fof(f38,plain,(
% 10.61/1.86 ![X0]: (sum(additive_identity,X0,X0)|~defined(X0))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f3])).
% 10.61/1.86 fof(f39,plain,(
% 10.61/1.86 ![X0]: (sum(additive_inverse(X0),X0,additive_identity)|~defined(X0))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f4])).
% 10.61/1.86 fof(f40,plain,(
% 10.61/1.86 ![X0,X1,X2]: (sum(X0,X1,X2)|~sum(X1,X0,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f5])).
% 10.61/1.86 fof(f41,plain,(
% 10.61/1.86 ![W,U,Z]: ((![V,Y]: ((![X]: (product(X,V,W)|~product(X,Y,U)))|~product(Y,Z,V)))|~product(U,Z,W))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f6])).
% 10.61/1.86 fof(f42,plain,(
% 10.61/1.86 ![X0,X1,X2,X3,X4,X5]: (product(X0,X1,X2)|~product(X0,X3,X4)|~product(X3,X5,X1)|~product(X4,X5,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f41])).
% 10.61/1.86 fof(f43,plain,(
% 10.61/1.86 ![W,X,V]: ((![Z,Y]: ((![U]: (product(U,Z,W)|~product(X,Y,U)))|~product(Y,Z,V)))|~product(X,V,W))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f7])).
% 10.61/1.86 fof(f44,plain,(
% 10.61/1.86 ![X0,X1,X2,X3,X4,X5]: (product(X0,X1,X2)|~product(X3,X4,X0)|~product(X4,X1,X5)|~product(X3,X5,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f43])).
% 10.61/1.86 fof(f45,plain,(
% 10.61/1.86 ![X0]: (product(multiplicative_identity,X0,X0)|~defined(X0))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f8])).
% 10.61/1.86 fof(f46,plain,(
% 10.61/1.86 ![X0]: (product(multiplicative_inverse(X0),X0,multiplicative_identity)|sum(additive_identity,X0,additive_identity)|~defined(X0))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f9])).
% 10.61/1.86 fof(f47,plain,(
% 10.61/1.86 ![X0,X1,X2]: (product(X0,X1,X2)|~product(X1,X0,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f10])).
% 10.61/1.86 fof(f48,plain,(
% 10.61/1.86 ![D,Y,Z]: ((![C,X]: ((![B,A]: ((sum(C,D,B)|~sum(X,Y,A))|~product(A,Z,B)))|~product(X,Z,C)))|~product(Y,Z,D))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f11])).
% 10.61/1.86 fof(f49,plain,(
% 10.61/1.86 ![X0,X1,X2,X3,X4,X5,X6]: (sum(X0,X1,X2)|~sum(X3,X4,X5)|~product(X5,X6,X2)|~product(X3,X6,X0)|~product(X4,X6,X1))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f48])).
% 10.61/1.86 fof(f50,plain,(
% 10.61/1.86 ![B,C,D]: ((![Z,Y]: ((![X]: ((![A]: (product(A,Z,B)|~sum(X,Y,A)))|~product(X,Z,C)))|~product(Y,Z,D)))|~sum(C,D,B))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f12])).
% 10.61/1.86 fof(f51,plain,(
% 10.61/1.86 ![X0,X1,X2,X3,X4,X5,X6]: (product(X0,X1,X2)|~sum(X3,X4,X0)|~product(X3,X1,X5)|~product(X4,X1,X6)|~sum(X5,X6,X2))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f50])).
% 10.61/1.86 fof(f54,plain,(
% 10.61/1.86 defined(additive_identity)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f14])).
% 10.61/1.86 fof(f55,plain,(
% 10.61/1.86 ![X0]: (defined(additive_inverse(X0))|~defined(X0))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f15])).
% 10.61/1.86 fof(f58,plain,(
% 10.61/1.86 defined(multiplicative_identity)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f17])).
% 10.61/1.86 fof(f67,plain,(
% 10.61/1.86 ![Y]: ((![X]: ((less_or_equal(X,Y)|less_or_equal(Y,X))|~defined(X)))|~defined(Y))),
% 10.61/1.86 inference(miniscoping,[status(thm)],[f23])).
% 10.61/1.86 fof(f68,plain,(
% 10.61/1.86 ![X0,X1]: (less_or_equal(X0,X1)|less_or_equal(X1,X0)|~defined(X0)|~defined(X1))),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f67])).
% 10.61/1.86 fof(f72,plain,(
% 10.61/1.86 ~sum(additive_identity,additive_identity,multiplicative_identity)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f26])).
% 10.61/1.86 fof(f73,plain,(
% 10.61/1.86 defined(a)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f27])).
% 10.61/1.86 fof(f74,plain,(
% 10.61/1.86 defined(b)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f28])).
% 10.61/1.86 fof(f75,plain,(
% 10.61/1.86 defined(c)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f29])).
% 10.61/1.86 fof(f76,plain,(
% 10.61/1.86 ~sum(additive_identity,a,additive_identity)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f30])).
% 10.61/1.86 fof(f77,plain,(
% 10.61/1.86 ~sum(additive_identity,b,additive_identity)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f31])).
% 10.61/1.86 fof(f78,plain,(
% 10.61/1.86 product(a,b,c)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f32])).
% 10.61/1.86 fof(f79,plain,(
% 10.61/1.86 sum(additive_identity,c,additive_identity)),
% 10.61/1.86 inference(cnf_transformation,[status(thm)],[f33])).
% 10.61/1.86 fof(f80,plain,(
% 10.61/1.86 defined(additive_inverse(multiplicative_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f55,f58])).
% 10.61/1.86 fof(f81,plain,(
% 10.61/1.86 defined(additive_inverse(c))),
% 10.61/1.86 inference(resolution,[status(thm)],[f55,f75])).
% 10.61/1.86 fof(f82,plain,(
% 10.61/1.86 defined(additive_inverse(b))),
% 10.61/1.86 inference(resolution,[status(thm)],[f55,f74])).
% 10.61/1.86 fof(f83,plain,(
% 10.61/1.86 defined(additive_inverse(a))),
% 10.61/1.86 inference(resolution,[status(thm)],[f55,f73])).
% 10.61/1.86 fof(f84,plain,(
% 10.61/1.86 defined(additive_inverse(additive_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f55,f54])).
% 10.61/1.86 fof(f85,plain,(
% 10.61/1.86 defined(additive_inverse(additive_inverse(multiplicative_identity)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f80,f55])).
% 10.61/1.86 fof(f86,plain,(
% 10.61/1.86 defined(additive_inverse(additive_inverse(c)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f81,f55])).
% 10.61/1.86 fof(f87,plain,(
% 10.61/1.86 defined(additive_inverse(additive_inverse(b)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f82,f55])).
% 10.61/1.86 fof(f88,plain,(
% 10.61/1.86 defined(additive_inverse(additive_inverse(a)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f83,f55])).
% 10.61/1.86 fof(f94,plain,(
% 10.61/1.86 sum(additive_identity,c,c)),
% 10.61/1.86 inference(resolution,[status(thm)],[f38,f75])).
% 10.61/1.86 fof(f95,plain,(
% 10.61/1.86 sum(additive_identity,b,b)),
% 10.61/1.86 inference(resolution,[status(thm)],[f38,f74])).
% 10.61/1.86 fof(f97,plain,(
% 10.61/1.86 sum(additive_identity,additive_identity,additive_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f38,f54])).
% 10.61/1.86 fof(f104,plain,(
% 10.61/1.86 sum(additive_inverse(b),b,additive_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f39,f74])).
% 10.61/1.86 fof(f110,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(multiplicative_identity))|less_or_equal(additive_inverse(multiplicative_identity),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f68,f80])).
% 10.61/1.86 fof(f111,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,multiplicative_identity)|less_or_equal(multiplicative_identity,X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f68,f58])).
% 10.61/1.86 fof(f479,plain,(
% 10.61/1.86 product(multiplicative_inverse(b),b,multiplicative_identity)|sum(additive_identity,b,additive_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f46,f74])).
% 10.61/1.86 fof(f480,plain,(
% 10.61/1.86 product(multiplicative_inverse(a),a,multiplicative_identity)|sum(additive_identity,a,additive_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f46,f73])).
% 10.61/1.86 fof(f524,definition,(
% 10.61/1.86 sQ89_spl <=> (product(multiplicative_inverse(b),b,multiplicative_identity))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f525,plain,(
% 10.61/1.86 product(multiplicative_inverse(b),b,multiplicative_identity)|~sQ89_spl),
% 10.61/1.86 inference(component_clause,[status(thm)],[f524])).
% 10.61/1.86 fof(f527,definition,(
% 10.61/1.86 sQ90_spl <=> (sum(additive_identity,b,additive_identity))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f528,plain,(
% 10.61/1.86 sum(additive_identity,b,additive_identity)|~sQ90_spl),
% 10.61/1.86 inference(component_clause,[status(thm)],[f527])).
% 10.61/1.86 fof(f530,plain,(
% 10.61/1.86 sQ89_spl|sQ90_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f479,f524,f527])).
% 10.61/1.86 fof(f531,definition,(
% 10.61/1.86 sQ91_spl <=> (product(multiplicative_inverse(a),a,multiplicative_identity))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f532,plain,(
% 10.61/1.86 product(multiplicative_inverse(a),a,multiplicative_identity)|~sQ91_spl),
% 10.61/1.86 inference(component_clause,[status(thm)],[f531])).
% 10.61/1.86 fof(f534,definition,(
% 10.61/1.86 sQ92_spl <=> (sum(additive_identity,a,additive_identity))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f535,plain,(
% 10.61/1.86 sum(additive_identity,a,additive_identity)|~sQ92_spl),
% 10.61/1.86 inference(component_clause,[status(thm)],[f534])).
% 10.61/1.86 fof(f537,plain,(
% 10.61/1.86 sQ91_spl|sQ92_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f480,f531,f534])).
% 10.61/1.86 fof(f590,plain,(
% 10.61/1.86 $false|~sQ92_spl),
% 10.61/1.86 inference(forward_subsumption_resolution,[status(thm)],[f535,f76])).
% 10.61/1.86 fof(f591,plain,(
% 10.61/1.86 ~sQ92_spl),
% 10.61/1.86 inference(contradiction_clause,[status(thm)],[f590])).
% 10.61/1.86 fof(f592,plain,(
% 10.61/1.86 $false|~sQ90_spl),
% 10.61/1.86 inference(forward_subsumption_resolution,[status(thm)],[f528,f77])).
% 10.61/1.86 fof(f593,plain,(
% 10.61/1.86 ~sQ90_spl),
% 10.61/1.86 inference(contradiction_clause,[status(thm)],[f592])).
% 10.61/1.86 fof(f598,plain,(
% 10.61/1.86 less_or_equal(multiplicative_identity,multiplicative_identity)|less_or_equal(multiplicative_identity,multiplicative_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f111,f58])).
% 10.61/1.86 fof(f613,definition,(
% 10.61/1.86 sQ106_spl <=> (less_or_equal(multiplicative_identity,multiplicative_identity))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f616,plain,(
% 10.61/1.86 sQ106_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f598,f613])).
% 10.61/1.86 fof(f624,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity))|less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f110,f80])).
% 10.61/1.86 fof(f633,definition,(
% 10.61/1.86 sQ107_spl <=> (less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity)))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f636,plain,(
% 10.61/1.86 sQ107_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f624,f633])).
% 10.61/1.86 fof(f642,plain,(
% 10.61/1.86 sum(c,additive_identity,additive_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f79,f40])).
% 10.61/1.86 fof(f644,plain,(
% 10.61/1.86 ![X0,X1,X2]: (sum(X0,c,X1)|~sum(X2,additive_identity,X0)|~sum(X2,additive_identity,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f79,f37])).
% 10.61/1.86 fof(f646,plain,(
% 10.61/1.86 ![X0,X1,X2]: (sum(X0,X1,additive_identity)|~sum(X0,X2,additive_identity)|~sum(X2,c,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f79,f35])).
% 10.61/1.86 fof(f648,plain,(
% 10.61/1.86 ![X0,X1,X2]: (sum(X0,additive_identity,X1)|~sum(X0,additive_identity,X2)|~sum(X2,c,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f79,f35])).
% 10.61/1.86 fof(f654,plain,(
% 10.61/1.86 ![X0]: (sum(X0,additive_identity,additive_identity)|~sum(X0,c,c))),
% 10.61/1.86 inference(resolution,[status(thm)],[f642,f35])).
% 10.61/1.86 fof(f668,plain,(
% 10.61/1.86 ![X0,X1,X2]: (product(X0,c,X1)|~product(X0,a,X2)|~product(X2,b,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f42,f78])).
% 10.61/1.86 fof(f669,plain,(
% 10.61/1.86 ![X0,X1,X2]: (product(X0,X1,c)|~product(X0,X2,a)|~product(X2,b,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f42,f78])).
% 10.61/1.86 fof(f686,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(additive_identity))|less_or_equal(additive_inverse(additive_identity),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f84,f68])).
% 10.61/1.86 fof(f689,plain,(
% 10.61/1.86 defined(additive_inverse(additive_inverse(additive_identity)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f84,f55])).
% 10.61/1.86 fof(f764,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity))|less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f686,f84])).
% 10.61/1.86 fof(f774,definition,(
% 10.61/1.86 sQ129_spl <=> (less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity)))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f777,plain,(
% 10.61/1.86 sQ129_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f764,f774])).
% 10.61/1.86 fof(f1055,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(additive_inverse(c)))|less_or_equal(additive_inverse(additive_inverse(c)),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f86,f68])).
% 10.61/1.86 fof(f1156,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(additive_inverse(c)),additive_inverse(additive_inverse(c)))|less_or_equal(additive_inverse(additive_inverse(c)),additive_inverse(additive_inverse(c)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1055,f86])).
% 10.61/1.86 fof(f1169,definition,(
% 10.61/1.86 sQ207_spl <=> (less_or_equal(additive_inverse(additive_inverse(c)),additive_inverse(additive_inverse(c))))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f1172,plain,(
% 10.61/1.86 sQ207_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f1156,f1169])).
% 10.61/1.86 fof(f1198,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(additive_inverse(b)))|less_or_equal(additive_inverse(additive_inverse(b)),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f87,f68])).
% 10.61/1.86 fof(f1306,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(additive_inverse(b)),additive_inverse(additive_inverse(b)))|less_or_equal(additive_inverse(additive_inverse(b)),additive_inverse(additive_inverse(b)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1198,f87])).
% 10.61/1.86 fof(f1320,definition,(
% 10.61/1.86 sQ237_spl <=> (less_or_equal(additive_inverse(additive_inverse(b)),additive_inverse(additive_inverse(b))))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f1323,plain,(
% 10.61/1.86 sQ237_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f1306,f1320])).
% 10.61/1.86 fof(f1335,plain,(
% 10.61/1.86 product(b,a,c)),
% 10.61/1.86 inference(resolution,[status(thm)],[f47,f78])).
% 10.61/1.86 fof(f1342,plain,(
% 10.61/1.86 ![X0,X1,X2]: (product(X0,c,X1)|~product(X0,b,X2)|~product(X2,a,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1335,f42])).
% 10.61/1.86 fof(f1364,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(additive_inverse(a)))|less_or_equal(additive_inverse(additive_inverse(a)),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f88,f68])).
% 10.61/1.86 fof(f1490,plain,(
% 10.61/1.86 ![X0]: (sum(X0,c,additive_identity)|~sum(X0,additive_identity,additive_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f94,f646])).
% 10.61/1.86 fof(f1503,plain,(
% 10.61/1.86 sum(b,additive_identity,b)),
% 10.61/1.86 inference(resolution,[status(thm)],[f95,f40])).
% 10.61/1.86 fof(f1527,plain,(
% 10.61/1.86 ![X0]: (sum(additive_identity,additive_identity,X0)|~sum(additive_identity,c,X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f97,f648])).
% 10.61/1.86 fof(f1572,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(additive_inverse(multiplicative_identity)))|less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f85,f68])).
% 10.61/1.86 fof(f1698,plain,(
% 10.61/1.86 product(multiplicative_identity,b,b)),
% 10.61/1.86 inference(resolution,[status(thm)],[f45,f74])).
% 10.61/1.86 fof(f1699,plain,(
% 10.61/1.86 product(multiplicative_identity,a,a)),
% 10.61/1.86 inference(resolution,[status(thm)],[f45,f73])).
% 10.61/1.86 fof(f1736,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a)))|less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1364,f88])).
% 10.61/1.86 fof(f1758,definition,(
% 10.61/1.86 sQ302_spl <=> (less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a))))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f1761,plain,(
% 10.61/1.86 sQ302_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f1736,f1758])).
% 10.61/1.86 fof(f1776,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity)))|less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1572,f85])).
% 10.61/1.86 fof(f1792,definition,(
% 10.61/1.86 sQ303_spl <=> (less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity))))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f1795,plain,(
% 10.61/1.86 sQ303_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f1776,f1792])).
% 10.61/1.86 fof(f1809,plain,(
% 10.61/1.86 sum(c,c,additive_identity)),
% 10.61/1.86 inference(resolution,[status(thm)],[f1490,f642])).
% 10.61/1.86 fof(f1814,plain,(
% 10.61/1.86 ![X0,X1,X2,X3]: (product(X0,X1,additive_identity)|~sum(X2,X3,X0)|~product(X2,X1,c)|~product(X3,X1,c))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1809,f51])).
% 10.61/1.86 fof(f1833,plain,(
% 10.61/1.86 sum(additive_identity,additive_identity,c)),
% 10.61/1.86 inference(resolution,[status(thm)],[f1527,f94])).
% 10.61/1.86 fof(f1843,plain,(
% 10.61/1.86 ![X0]: (sum(X0,c,c)|~sum(additive_identity,additive_identity,X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1833,f644])).
% 10.61/1.86 fof(f1846,plain,(
% 10.61/1.86 ![X0,X1,X2,X3]: (sum(X0,X1,X2)|~product(c,X3,X2)|~product(additive_identity,X3,X0)|~product(additive_identity,X3,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1833,f49])).
% 10.61/1.86 fof(f1851,plain,(
% 10.61/1.86 ![X0,X1,X2]: (sum(X0,X1,c)|~sum(X0,X2,additive_identity)|~sum(X2,additive_identity,X1))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1833,f35])).
% 10.61/1.86 fof(f1981,plain,(
% 10.61/1.86 sum(c,c,c)),
% 10.61/1.86 inference(resolution,[status(thm)],[f1843,f1833])).
% 10.61/1.86 fof(f2068,plain,(
% 10.61/1.86 ![X0]: (product(c,X0,additive_identity)|~product(c,X0,c)|~product(c,X0,c))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1814,f1981])).
% 10.61/1.86 fof(f2081,plain,(
% 10.61/1.86 ![X0]: (product(c,X0,additive_identity)|~product(c,X0,c))),
% 10.61/1.86 inference(duplicate_literals_removal,[status(thm)],[f2068])).
% 10.61/1.86 fof(f2284,definition,(
% 10.61/1.86 sQ318_spl <=> (sum(additive_identity,additive_identity,multiplicative_identity))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f2285,plain,(
% 10.61/1.86 sum(additive_identity,additive_identity,multiplicative_identity)|~sQ318_spl),
% 10.61/1.86 inference(component_clause,[status(thm)],[f2284])).
% 10.61/1.86 fof(f2328,plain,(
% 10.61/1.86 $false|~sQ318_spl),
% 10.61/1.86 inference(forward_subsumption_resolution,[status(thm)],[f2285,f72])).
% 10.61/1.86 fof(f2329,plain,(
% 10.61/1.86 ~sQ318_spl),
% 10.61/1.86 inference(contradiction_clause,[status(thm)],[f2328])).
% 10.61/1.86 fof(f2903,plain,(
% 10.61/1.86 ![X0]: (product(multiplicative_inverse(b),c,X0)|~product(multiplicative_identity,a,X0)|~sQ89_spl)),
% 10.61/1.86 inference(resolution,[status(thm)],[f525,f1342])).
% 10.61/1.86 fof(f2904,plain,(
% 10.61/1.86 ![X0]: (product(X0,multiplicative_identity,c)|~product(X0,multiplicative_inverse(b),a)|~sQ89_spl)),
% 10.61/1.86 inference(resolution,[status(thm)],[f525,f669])).
% 10.61/1.86 fof(f2972,plain,(
% 10.61/1.86 ![X0]: (less_or_equal(X0,additive_inverse(additive_inverse(additive_identity)))|less_or_equal(additive_inverse(additive_inverse(additive_identity)),X0)|~defined(X0))),
% 10.61/1.86 inference(resolution,[status(thm)],[f689,f68])).
% 10.61/1.86 fof(f3145,plain,(
% 10.61/1.86 less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity)))|less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity)))),
% 10.61/1.86 inference(resolution,[status(thm)],[f2972,f689])).
% 10.61/1.86 fof(f3162,definition,(
% 10.61/1.86 sQ374_spl <=> (less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity))))),
% 10.61/1.86 introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition])).
% 10.61/1.86 fof(f3165,plain,(
% 10.61/1.86 sQ374_spl),
% 10.61/1.86 inference(split_clause,[status(thm)],[f3145,f3162])).
% 10.61/1.86 fof(f3663,plain,(
% 10.61/1.86 ![X0]: (product(X0,c,b)|~product(X0,a,multiplicative_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1698,f668])).
% 10.61/1.86 fof(f3675,plain,(
% 10.61/1.86 product(multiplicative_inverse(b),c,a)|~sQ89_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f1699,f2903])).
% 10.61/1.86 fof(f4366,plain,(
% 10.61/1.86 product(multiplicative_inverse(a),c,b)|~sQ91_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f3663,f532])).
% 10.61/1.86 fof(f4371,plain,(
% 10.61/1.86 product(c,multiplicative_inverse(b),a)|~sQ89_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f3675,f47])).
% 10.61/1.86 fof(f4382,plain,(
% 10.61/1.86 product(c,multiplicative_inverse(a),b)|~sQ91_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f4366,f47])).
% 10.61/1.86 fof(f4390,plain,(
% 10.61/1.86 product(c,multiplicative_identity,c)|~sQ89_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f4371,f2904])).
% 10.61/1.86 fof(f4401,plain,(
% 10.61/1.86 product(c,multiplicative_identity,additive_identity)|~sQ89_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f4390,f2081])).
% 10.61/1.86 fof(f4462,plain,(
% 10.61/1.86 product(multiplicative_identity,c,additive_identity)|~sQ89_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f4401,f47])).
% 10.61/1.86 fof(f4577,plain,(
% 10.61/1.86 ![X0,X1,X2]: (product(X0,multiplicative_inverse(a),X1)|~product(X2,c,X0)|~product(X2,b,X1)|~sQ91_spl)),
% 10.61/1.86 inference(resolution,[status(thm)],[f4382,f44])).
% 10.61/1.86 fof(f4764,plain,(
% 10.61/1.86 ![X0]: (product(additive_identity,multiplicative_inverse(a),X0)|~product(multiplicative_identity,b,X0)|~sQ91_spl|~sQ89_spl)),
% 10.61/1.86 inference(resolution,[status(thm)],[f4577,f4462])).
% 10.61/1.86 fof(f5074,plain,(
% 10.61/1.86 product(additive_identity,multiplicative_inverse(a),b)|~sQ91_spl|~sQ89_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f4764,f1698])).
% 10.61/1.86 fof(f5076,plain,(
% 10.61/1.86 ![X0]: (sum(b,b,X0)|~product(c,multiplicative_inverse(a),X0)|~sQ91_spl|~sQ89_spl)),
% 10.61/1.86 inference(resolution,[status(thm)],[f5074,f1846])).
% 10.61/1.86 fof(f5112,plain,(
% 10.61/1.86 sum(b,b,b)|~sQ89_spl|~sQ91_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f5076,f4382])).
% 10.61/1.86 fof(f5294,plain,(
% 10.61/1.86 ![X0]: (sum(X0,b,c)|~sum(X0,b,additive_identity))),
% 10.61/1.86 inference(resolution,[status(thm)],[f1503,f1851])).
% 10.61/1.86 fof(f5644,plain,(
% 10.61/1.86 sum(additive_inverse(b),b,c)),
% 10.61/1.86 inference(resolution,[status(thm)],[f5294,f104])).
% 10.61/1.86 fof(f5654,plain,(
% 10.61/1.86 sum(b,additive_inverse(b),c)),
% 10.61/1.86 inference(resolution,[status(thm)],[f5644,f40])).
% 10.61/1.86 fof(f5674,plain,(
% 10.61/1.86 ![X0]: (sum(X0,c,c)|~sum(X0,b,b))),
% 10.61/1.86 inference(resolution,[status(thm)],[f5654,f35])).
% 10.61/1.86 fof(f6588,plain,(
% 10.61/1.86 sum(b,c,c)|~sQ89_spl|~sQ91_spl),
% 10.61/1.86 inference(resolution,[status(thm)],[f5674,f5112])).
% 10.61/1.86 fof(f6603,plain,(
% 10.61/1.86 sum(b,additive_identity,additive_identity)|~sQ89_spl|~sQ91_spl),
% 10.61/1.88 inference(resolution,[status(thm)],[f6588,f654])).
% 10.61/1.88 fof(f7020,plain,(
% 10.61/1.88 sum(additive_identity,b,additive_identity)|~sQ89_spl|~sQ91_spl),
% 10.61/1.88 inference(resolution,[status(thm)],[f6603,f40])).
% 10.61/1.88 fof(f7035,plain,(
% 10.61/1.88 sQ90_spl|~sQ89_spl|~sQ91_spl),
% 10.61/1.88 inference(split_clause,[status(thm)],[f7020,f527,f524,f531])).
% 10.61/1.88 fof(f7036,plain,(
% 10.61/1.88 $false),
% 10.61/1.88 inference(sat_refutation,[status(thm)],[f530,f537,f591,f593,f616,f636,f777,f1172,f1323,f1761,f1795,f2329,f3165,f7035])).
% 10.61/1.88 % SZS output end CNFRefutation for theBenchmark.p
% 10.61/1.90 % Elapsed time: 1.443249 seconds
% 10.61/1.90 % CPU time: 11.072298 seconds
% 10.61/1.90 % Total memory used: 86.600 MB
% 10.61/1.90 % Net memory used: 81.304 MB
%------------------------------------------------------------------------------