%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : FLD031-5 : 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 : n015.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 12:22:22 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 15:42:22 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.24/0.58 % Refutation found
% 0.24/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.58 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.58 fof(f6,axiom,(
% 0.24/0.58 (![X,V,W,Y,U,Z]: (( product(X,V,W)| ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f7,axiom,(
% 0.24/0.58 (![U,Z,W,X,Y,V]: (( product(U,Z,W)| ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(X,V,W) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f8,axiom,(
% 0.24/0.58 (![X]: (( product(multiplicative_identity,X,X)| ~ defined(X) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f9,axiom,(
% 0.24/0.58 (![X]: (( product(multiplicative_inverse(X),X,multiplicative_identity)| sum(additive_identity,X,additive_identity)| ~ defined(X) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f10,axiom,(
% 0.24/0.58 (![Y,X,Z]: (( product(Y,X,Z)| ~ product(X,Y,Z) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f14,axiom,(
% 0.24/0.58 defined(additive_identity) ),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f15,axiom,(
% 0.24/0.58 (![X]: (( defined(additive_inverse(X))| ~ defined(X) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f17,axiom,(
% 0.24/0.58 defined(multiplicative_identity) ),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f18,axiom,(
% 0.24/0.58 (![X]: (( defined(multiplicative_inverse(X))| ~ defined(X)| sum(additive_identity,X,additive_identity) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f23,axiom,(
% 0.24/0.58 (![X,Y]: (( less_or_equal(X,Y)| less_or_equal(Y,X)| ~ defined(X)| ~ defined(Y) ) ))),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f27,hypothesis,(
% 0.24/0.58 defined(a) ),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f28,negated_conjecture,(
% 0.24/0.58 product(multiplicative_identity,a,multiplicative_identity) ),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f29,negated_conjecture,(
% 0.24/0.58 ~ sum(additive_identity,a,additive_identity) ),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f30,negated_conjecture,(
% 0.24/0.58 ~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)) ),
% 0.24/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.58 fof(f38,plain,(
% 0.24/0.58 ![W,U,Z]: ((![V,Y]: ((![X]: (product(X,V,W)|~product(X,Y,U)))|~product(Y,Z,V)))|~product(U,Z,W))),
% 0.24/0.58 inference(miniscoping,[status(thm)],[f6])).
% 0.24/0.58 fof(f39,plain,(
% 0.24/0.58 ![X0,X1,X2,X3,X4,X5]: (product(X0,X1,X2)|~product(X0,X3,X4)|~product(X3,X5,X1)|~product(X4,X5,X2))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f38])).
% 0.24/0.58 fof(f40,plain,(
% 0.24/0.58 ![W,X,V]: ((![Z,Y]: ((![U]: (product(U,Z,W)|~product(X,Y,U)))|~product(Y,Z,V)))|~product(X,V,W))),
% 0.24/0.58 inference(miniscoping,[status(thm)],[f7])).
% 0.24/0.58 fof(f41,plain,(
% 0.24/0.58 ![X0,X1,X2,X3,X4,X5]: (product(X0,X1,X2)|~product(X3,X4,X0)|~product(X4,X1,X5)|~product(X3,X5,X2))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f40])).
% 0.24/0.58 fof(f42,plain,(
% 0.24/0.58 ![X0]: (product(multiplicative_identity,X0,X0)|~defined(X0))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f8])).
% 0.24/0.58 fof(f43,plain,(
% 0.24/0.58 ![X0]: (product(multiplicative_inverse(X0),X0,multiplicative_identity)|sum(additive_identity,X0,additive_identity)|~defined(X0))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f9])).
% 0.24/0.58 fof(f44,plain,(
% 0.24/0.58 ![X0,X1,X2]: (product(X0,X1,X2)|~product(X1,X0,X2))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f10])).
% 0.24/0.58 fof(f51,plain,(
% 0.24/0.58 defined(additive_identity)),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f14])).
% 0.24/0.58 fof(f52,plain,(
% 0.24/0.58 ![X0]: (defined(additive_inverse(X0))|~defined(X0))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f15])).
% 0.24/0.58 fof(f55,plain,(
% 0.24/0.58 defined(multiplicative_identity)),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f17])).
% 0.24/0.58 fof(f56,plain,(
% 0.24/0.58 ![X0]: (defined(multiplicative_inverse(X0))|~defined(X0)|sum(additive_identity,X0,additive_identity))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f18])).
% 0.24/0.58 fof(f64,plain,(
% 0.24/0.58 ![Y]: ((![X]: ((less_or_equal(X,Y)|less_or_equal(Y,X))|~defined(X)))|~defined(Y))),
% 0.24/0.58 inference(miniscoping,[status(thm)],[f23])).
% 0.24/0.58 fof(f65,plain,(
% 0.24/0.58 ![X0,X1]: (less_or_equal(X0,X1)|less_or_equal(X1,X0)|~defined(X0)|~defined(X1))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f64])).
% 0.24/0.58 fof(f70,plain,(
% 0.24/0.58 defined(a)),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f27])).
% 0.24/0.58 fof(f71,plain,(
% 0.24/0.58 product(multiplicative_identity,a,multiplicative_identity)),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f28])).
% 0.24/0.58 fof(f72,plain,(
% 0.24/0.58 ~sum(additive_identity,a,additive_identity)),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f29])).
% 0.24/0.58 fof(f73,plain,(
% 0.24/0.58 ~product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a))),
% 0.24/0.58 inference(cnf_transformation,[status(thm)],[f30])).
% 0.24/0.58 fof(f77,plain,(
% 0.24/0.58 defined(additive_inverse(a))),
% 0.24/0.58 inference(resolution,[status(thm)],[f52,f70])).
% 0.24/0.58 fof(f78,plain,(
% 0.24/0.58 defined(additive_inverse(multiplicative_identity))),
% 0.24/0.58 inference(resolution,[status(thm)],[f52,f55])).
% 0.24/0.58 fof(f79,plain,(
% 0.24/0.58 defined(additive_inverse(additive_identity))),
% 0.24/0.58 inference(resolution,[status(thm)],[f52,f51])).
% 0.24/0.58 fof(f80,plain,(
% 0.24/0.58 defined(additive_inverse(additive_inverse(a)))),
% 0.24/0.58 inference(resolution,[status(thm)],[f77,f52])).
% 0.24/0.58 fof(f86,plain,(
% 0.24/0.58 ![X0,X1,X2]: (product(multiplicative_identity,X0,X1)|~product(a,X2,X0)|~product(multiplicative_identity,X2,X1))),
% 0.24/0.58 inference(resolution,[status(thm)],[f39,f71])).
% 0.24/0.58 fof(f89,plain,(
% 0.24/0.58 product(multiplicative_identity,a,a)),
% 0.24/0.58 inference(resolution,[status(thm)],[f42,f70])).
% 0.24/0.58 fof(f92,plain,(
% 0.24/0.58 product(a,multiplicative_identity,multiplicative_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f44,f71])).
% 0.24/0.58 fof(f94,plain,(
% 0.24/0.58 defined(multiplicative_inverse(a))|sum(additive_identity,a,additive_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f56,f70])).
% 0.24/0.58 fof(f104,definition,(
% 0.24/0.58 sQ2_spl <=> (defined(multiplicative_inverse(a)))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f105,plain,(
% 0.24/0.58 defined(multiplicative_inverse(a))|~sQ2_spl),
% 0.24/0.58 inference(component_clause,[status(thm)],[f104])).
% 0.24/0.58 fof(f107,definition,(
% 0.24/0.58 sQ3_spl <=> (sum(additive_identity,a,additive_identity))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f108,plain,(
% 0.24/0.58 sum(additive_identity,a,additive_identity)|~sQ3_spl),
% 0.24/0.58 inference(component_clause,[status(thm)],[f107])).
% 0.24/0.58 fof(f110,plain,(
% 0.24/0.58 sQ2_spl|sQ3_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f94,f104,f107])).
% 0.24/0.58 fof(f126,plain,(
% 0.24/0.58 product(multiplicative_inverse(a),a,multiplicative_identity)|sum(additive_identity,a,additive_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f43,f70])).
% 0.24/0.58 fof(f133,definition,(
% 0.24/0.58 sQ9_spl <=> (product(multiplicative_inverse(a),a,multiplicative_identity))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f134,plain,(
% 0.24/0.58 product(multiplicative_inverse(a),a,multiplicative_identity)|~sQ9_spl),
% 0.24/0.58 inference(component_clause,[status(thm)],[f133])).
% 0.24/0.58 fof(f136,plain,(
% 0.24/0.58 sQ9_spl|sQ3_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f126,f133,f107])).
% 0.24/0.58 fof(f145,plain,(
% 0.24/0.58 $false|~sQ3_spl),
% 0.24/0.58 inference(forward_subsumption_resolution,[status(thm)],[f108,f72])).
% 0.24/0.58 fof(f146,plain,(
% 0.24/0.58 ~sQ3_spl),
% 0.24/0.58 inference(contradiction_clause,[status(thm)],[f145])).
% 0.24/0.58 fof(f147,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_inverse(a),X0)|less_or_equal(X0,additive_inverse(a))|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f65,f77])).
% 0.24/0.58 fof(f148,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(a,X0)|less_or_equal(X0,a)|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f65,f70])).
% 0.24/0.58 fof(f149,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(multiplicative_identity,X0)|less_or_equal(X0,multiplicative_identity)|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f65,f55])).
% 0.24/0.58 fof(f150,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_identity,X0)|less_or_equal(X0,additive_identity)|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f65,f51])).
% 0.24/0.58 fof(f152,plain,(
% 0.24/0.58 less_or_equal(a,a)|less_or_equal(a,a)),
% 0.24/0.58 inference(resolution,[status(thm)],[f148,f70])).
% 0.24/0.58 fof(f162,definition,(
% 0.24/0.58 sQ14_spl <=> (less_or_equal(a,a))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f165,plain,(
% 0.24/0.58 sQ14_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f152,f162])).
% 0.24/0.58 fof(f182,plain,(
% 0.24/0.58 less_or_equal(multiplicative_identity,multiplicative_identity)|less_or_equal(multiplicative_identity,multiplicative_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f149,f55])).
% 0.24/0.58 fof(f192,definition,(
% 0.24/0.58 sQ21_spl <=> (less_or_equal(multiplicative_identity,multiplicative_identity))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f195,plain,(
% 0.24/0.58 sQ21_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f182,f192])).
% 0.24/0.58 fof(f206,plain,(
% 0.24/0.58 less_or_equal(additive_identity,additive_identity)|less_or_equal(additive_identity,additive_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f150,f51])).
% 0.24/0.58 fof(f216,definition,(
% 0.24/0.58 sQ26_spl <=> (less_or_equal(additive_identity,additive_identity))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f219,plain,(
% 0.24/0.58 sQ26_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f206,f216])).
% 0.24/0.58 fof(f220,plain,(
% 0.24/0.58 less_or_equal(additive_inverse(a),additive_inverse(a))|less_or_equal(additive_inverse(a),additive_inverse(a))),
% 0.24/0.58 inference(resolution,[status(thm)],[f147,f77])).
% 0.24/0.58 fof(f224,definition,(
% 0.24/0.58 sQ27_spl <=> (less_or_equal(additive_inverse(a),additive_inverse(a)))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f227,plain,(
% 0.24/0.58 sQ27_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f220,f224])).
% 0.24/0.58 fof(f234,plain,(
% 0.24/0.58 ![X0,X1,X2]: (product(multiplicative_identity,X0,X1)|~product(multiplicative_identity,X0,X2)|~product(a,X2,X1))),
% 0.24/0.58 inference(resolution,[status(thm)],[f92,f41])).
% 0.24/0.58 fof(f235,plain,(
% 0.24/0.58 ![X0,X1,X2]: (product(a,X0,X1)|~product(multiplicative_identity,X2,X0)|~product(multiplicative_identity,X2,X1))),
% 0.24/0.58 inference(resolution,[status(thm)],[f92,f39])).
% 0.24/0.58 fof(f242,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_inverse(multiplicative_identity),X0)|less_or_equal(X0,additive_inverse(multiplicative_identity))|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f78,f65])).
% 0.24/0.58 fof(f247,plain,(
% 0.24/0.58 defined(additive_inverse(additive_inverse(multiplicative_identity)))),
% 0.24/0.58 inference(resolution,[status(thm)],[f78,f52])).
% 0.24/0.58 fof(f288,plain,(
% 0.24/0.58 less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity))|less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity))),
% 0.24/0.58 inference(resolution,[status(thm)],[f242,f78])).
% 0.24/0.58 fof(f293,definition,(
% 0.24/0.58 sQ39_spl <=> (less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity)))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f296,plain,(
% 0.24/0.58 sQ39_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f288,f293])).
% 0.24/0.58 fof(f306,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_inverse(additive_identity),X0)|less_or_equal(X0,additive_inverse(additive_identity))|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f79,f65])).
% 0.24/0.58 fof(f311,plain,(
% 0.24/0.58 defined(additive_inverse(additive_inverse(additive_identity)))),
% 0.24/0.58 inference(resolution,[status(thm)],[f79,f52])).
% 0.24/0.58 fof(f359,plain,(
% 0.24/0.58 less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity))|less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity))),
% 0.24/0.58 inference(resolution,[status(thm)],[f306,f79])).
% 0.24/0.58 fof(f365,definition,(
% 0.24/0.58 sQ53_spl <=> (less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity)))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f368,plain,(
% 0.24/0.58 sQ53_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f359,f365])).
% 0.24/0.58 fof(f383,plain,(
% 0.24/0.58 product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a))|~sQ2_spl),
% 0.24/0.58 inference(resolution,[status(thm)],[f105,f42])).
% 0.24/0.58 fof(f487,plain,(
% 0.24/0.58 ![X0]: (product(a,a,X0)|~product(multiplicative_identity,a,X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f89,f235])).
% 0.24/0.58 fof(f493,plain,(
% 0.24/0.58 product(a,a,multiplicative_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f487,f71])).
% 0.24/0.58 fof(f502,plain,(
% 0.24/0.58 ![X0]: (product(multiplicative_identity,multiplicative_identity,X0)|~product(multiplicative_identity,a,X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f493,f86])).
% 0.24/0.58 fof(f513,plain,(
% 0.24/0.58 product(multiplicative_identity,multiplicative_identity,multiplicative_identity)),
% 0.24/0.58 inference(resolution,[status(thm)],[f502,f71])).
% 0.24/0.58 fof(f522,plain,(
% 0.24/0.58 ![X0]: (product(multiplicative_identity,multiplicative_identity,X0)|~product(a,multiplicative_identity,X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f513,f234])).
% 0.24/0.58 fof(f648,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_inverse(additive_inverse(a)),X0)|less_or_equal(X0,additive_inverse(additive_inverse(a)))|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f80,f65])).
% 0.24/0.58 fof(f781,plain,(
% 0.24/0.58 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)))),
% 0.24/0.58 inference(resolution,[status(thm)],[f648,f80])).
% 0.24/0.58 fof(f789,definition,(
% 0.24/0.58 sQ91_spl <=> (less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a))))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f792,plain,(
% 0.24/0.58 sQ91_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f781,f789])).
% 0.24/0.58 fof(f895,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),X0)|less_or_equal(X0,additive_inverse(additive_inverse(multiplicative_identity)))|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f247,f65])).
% 0.24/0.58 fof(f970,plain,(
% 0.24/0.58 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)))),
% 0.24/0.58 inference(resolution,[status(thm)],[f895,f247])).
% 0.24/0.58 fof(f979,definition,(
% 0.24/0.58 sQ113_spl <=> (less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity))))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f982,plain,(
% 0.24/0.58 sQ113_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f970,f979])).
% 0.24/0.58 fof(f1029,plain,(
% 0.24/0.58 ![X0]: (less_or_equal(additive_inverse(additive_inverse(additive_identity)),X0)|less_or_equal(X0,additive_inverse(additive_inverse(additive_identity)))|~defined(X0))),
% 0.24/0.58 inference(resolution,[status(thm)],[f311,f65])).
% 0.24/0.58 fof(f1111,plain,(
% 0.24/0.58 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)))),
% 0.24/0.58 inference(resolution,[status(thm)],[f1029,f311])).
% 0.24/0.58 fof(f1121,definition,(
% 0.24/0.58 sQ138_spl <=> (less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity))))),
% 0.24/0.58 introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition])).
% 0.24/0.58 fof(f1124,plain,(
% 0.24/0.58 sQ138_spl),
% 0.24/0.58 inference(split_clause,[status(thm)],[f1111,f1121])).
% 0.24/0.58 fof(f1528,plain,(
% 0.24/0.58 ![X0]: (product(a,multiplicative_inverse(a),X0)|~product(multiplicative_identity,multiplicative_inverse(a),X0)|~sQ2_spl)),
% 0.24/0.58 inference(resolution,[status(thm)],[f383,f235])).
% 0.24/0.58 fof(f1678,plain,(
% 0.24/0.58 product(a,multiplicative_inverse(a),multiplicative_inverse(a))|~sQ2_spl),
% 0.24/0.58 inference(resolution,[status(thm)],[f1528,f383])).
% 0.24/0.58 fof(f1693,plain,(
% 0.24/0.58 product(multiplicative_inverse(a),a,multiplicative_inverse(a))|~sQ2_spl),
% 0.24/0.58 inference(resolution,[status(thm)],[f1678,f44])).
% 0.24/0.58 fof(f1695,plain,(
% 0.24/0.58 ![X0,X1,X2]: (product(a,X0,X1)|~product(multiplicative_inverse(a),X2,X0)|~product(multiplicative_inverse(a),X2,X1)|~sQ2_spl)),
% 0.24/0.58 inference(resolution,[status(thm)],[f1678,f39])).
% 0.24/0.58 fof(f1764,plain,(
% 0.24/0.58 ![X0]: (product(a,multiplicative_identity,X0)|~product(multiplicative_inverse(a),a,X0)|~sQ2_spl|~sQ9_spl)),
% 0.24/0.58 inference(resolution,[status(thm)],[f1695,f134])).
% 0.24/0.58 fof(f1808,plain,(
% 0.24/0.58 product(a,multiplicative_identity,multiplicative_inverse(a))|~sQ9_spl|~sQ2_spl),
% 0.24/0.58 inference(resolution,[status(thm)],[f1764,f1693])).
% 0.24/0.58 fof(f1819,plain,(
% 0.24/0.58 product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a))|~sQ9_spl|~sQ2_spl),
% 0.24/0.59 inference(resolution,[status(thm)],[f1808,f522])).
% 0.24/0.59 fof(f1841,plain,(
% 0.24/0.59 $false|~sQ9_spl|~sQ2_spl),
% 0.24/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1819,f73])).
% 0.24/0.59 fof(f1842,plain,(
% 0.24/0.59 ~sQ9_spl|~sQ2_spl),
% 0.24/0.59 inference(contradiction_clause,[status(thm)],[f1841])).
% 0.24/0.59 fof(f1843,plain,(
% 0.24/0.59 $false),
% 0.24/0.59 inference(sat_refutation,[status(thm)],[f110,f136,f146,f165,f195,f219,f227,f296,f368,f792,f982,f1124,f1842])).
% 0.24/0.59 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.63 % Elapsed time: 0.161323 seconds
% 0.24/0.63 % CPU time: 0.664925 seconds
% 0.24/0.63 % Total memory used: 17.476 MB
% 0.24/0.63 % Net memory used: 17.045 MB
%------------------------------------------------------------------------------