%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : FLD031-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:22:21 PM UTC 2026
% Result : Unsatisfiable 13.84s 2.27s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD031-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n003.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 15:40:46 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 13.84/2.27 % Refutation found
% 13.84/2.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.84/2.27 % SZS output start CNFRefutation for theBenchmark
% 13.84/2.27 fof(f6,axiom,(
% 13.84/2.27 (![X]: (( equalish(multiply(multiplicative_identity,X),X)| ~ defined(X) ) ))),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f7,axiom,(
% 13.84/2.27 (![X]: (( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)| ~ defined(X)| equalish(X,additive_identity) ) ))),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f15,axiom,(
% 13.84/2.27 (![X]: (( defined(multiplicative_inverse(X))| ~ defined(X)| equalish(X,additive_identity) ) ))),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f22,axiom,(
% 13.84/2.27 (![X,Y]: (( equalish(X,Y)| ~ equalish(Y,X) ) ))),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f23,axiom,(
% 13.84/2.27 (![X,Z,Y]: (( equalish(X,Z)| ~ equalish(X,Y)| ~ equalish(Y,Z) ) ))),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f25,axiom,(
% 13.84/2.27 (![X,Z,Y]: (( equalish(multiply(X,Z),multiply(Y,Z))| ~ defined(Z)| ~ equalish(X,Y) ) ))),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f28,hypothesis,(
% 13.84/2.27 defined(a) ),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f29,negated_conjecture,(
% 13.84/2.27 equalish(a,multiplicative_identity) ),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f30,negated_conjecture,(
% 13.84/2.27 ~ equalish(a,additive_identity) ),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f31,negated_conjecture,(
% 13.84/2.27 ~ equalish(multiplicative_inverse(a),multiplicative_identity) ),
% 13.84/2.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f40,plain,(
% 13.84/2.27 ![X0]: (equalish(multiply(multiplicative_identity,X0),X0)|~defined(X0))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f6])).
% 13.84/2.27 fof(f41,plain,(
% 13.84/2.27 ![X0]: (equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)|~defined(X0)|equalish(X0,additive_identity))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f7])).
% 13.84/2.27 fof(f53,plain,(
% 13.84/2.27 ![X0]: (defined(multiplicative_inverse(X0))|~defined(X0)|equalish(X0,additive_identity))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f15])).
% 13.84/2.27 fof(f64,plain,(
% 13.84/2.27 ![X0,X1]: (equalish(X0,X1)|~equalish(X1,X0))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f22])).
% 13.84/2.27 fof(f65,plain,(
% 13.84/2.27 ![Z,Y]: ((![X]: (equalish(X,Z)|~equalish(X,Y)))|~equalish(Y,Z))),
% 13.84/2.27 inference(miniscoping,[status(thm)],[f23])).
% 13.84/2.27 fof(f66,plain,(
% 13.84/2.27 ![X0,X1,X2]: (equalish(X0,X1)|~equalish(X0,X2)|~equalish(X2,X1))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f65])).
% 13.84/2.27 fof(f69,plain,(
% 13.84/2.27 ![X,Y]: ((![Z]: (equalish(multiply(X,Z),multiply(Y,Z))|~defined(Z)))|~equalish(X,Y))),
% 13.84/2.27 inference(miniscoping,[status(thm)],[f25])).
% 13.84/2.27 fof(f70,plain,(
% 13.84/2.27 ![X0,X1,X2]: (equalish(multiply(X0,X1),multiply(X2,X1))|~defined(X1)|~equalish(X0,X2))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f69])).
% 13.84/2.27 fof(f74,plain,(
% 13.84/2.27 defined(a)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f28])).
% 13.84/2.27 fof(f75,plain,(
% 13.84/2.27 equalish(a,multiplicative_identity)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f29])).
% 13.84/2.27 fof(f76,plain,(
% 13.84/2.27 ~equalish(a,additive_identity)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f30])).
% 13.84/2.27 fof(f77,plain,(
% 13.84/2.27 ~equalish(multiplicative_inverse(a),multiplicative_identity)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f31])).
% 13.84/2.27 fof(f79,plain,(
% 13.84/2.27 ~equalish(additive_identity,a)),
% 13.84/2.27 inference(resolution,[status(thm)],[f64,f76])).
% 13.84/2.27 fof(f84,plain,(
% 13.84/2.27 ![X0]: (~equalish(multiplicative_inverse(a),X0)|~equalish(X0,multiplicative_identity))),
% 13.84/2.27 inference(resolution,[status(thm)],[f66,f77])).
% 13.84/2.27 fof(f87,plain,(
% 13.84/2.27 ![X0]: (~equalish(additive_identity,X0)|~equalish(X0,a))),
% 13.84/2.27 inference(resolution,[status(thm)],[f66,f79])).
% 13.84/2.27 fof(f95,plain,(
% 13.84/2.27 ![X0]: (~equalish(X0,a)|~equalish(X0,additive_identity))),
% 13.84/2.27 inference(resolution,[status(thm)],[f87,f64])).
% 13.84/2.27 fof(f102,plain,(
% 13.84/2.27 ![X0]: (~equalish(X0,multiplicative_identity)|~equalish(X0,multiplicative_inverse(a)))),
% 13.84/2.27 inference(resolution,[status(thm)],[f84,f64])).
% 13.84/2.27 fof(f121,plain,(
% 13.84/2.27 ~equalish(multiply(multiplicative_identity,a),additive_identity)|~defined(a)),
% 13.84/2.27 inference(resolution,[status(thm)],[f95,f40])).
% 13.84/2.27 fof(f125,definition,(
% 13.84/2.27 sQ3_spl <=> (equalish(multiply(multiplicative_identity,a),additive_identity))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f127,plain,(
% 13.84/2.27 ~equalish(multiply(multiplicative_identity,a),additive_identity)|sQ3_spl),
% 13.84/2.27 inference(component_clause,[status(thm)],[f125])).
% 13.84/2.27 fof(f128,definition,(
% 13.84/2.27 sQ4_spl <=> (defined(a))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f130,plain,(
% 13.84/2.27 ~defined(a)|sQ4_spl),
% 13.84/2.27 inference(component_clause,[status(thm)],[f128])).
% 13.84/2.27 fof(f131,plain,(
% 13.84/2.27 ~sQ3_spl|~sQ4_spl),
% 13.84/2.27 inference(split_clause,[status(thm)],[f121,f125,f128])).
% 13.84/2.27 fof(f136,plain,(
% 13.84/2.27 $false|sQ4_spl),
% 13.84/2.27 inference(forward_subsumption_resolution,[status(thm)],[f130,f74])).
% 13.84/2.27 fof(f137,plain,(
% 13.84/2.27 sQ4_spl),
% 13.84/2.27 inference(contradiction_clause,[status(thm)],[f136])).
% 13.84/2.27 fof(f160,plain,(
% 13.84/2.27 ![X0]: (~equalish(multiply(multiplicative_identity,a),X0)|~equalish(X0,additive_identity)|sQ3_spl)),
% 13.84/2.27 inference(resolution,[status(thm)],[f127,f66])).
% 13.84/2.27 fof(f176,plain,(
% 13.84/2.27 defined(multiplicative_inverse(a))|equalish(a,additive_identity)),
% 13.84/2.27 inference(resolution,[status(thm)],[f74,f53])).
% 13.84/2.27 fof(f179,definition,(
% 13.84/2.27 sQ10_spl <=> (defined(multiplicative_inverse(a)))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f182,definition,(
% 13.84/2.27 sQ11_spl <=> (equalish(a,additive_identity))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f185,plain,(
% 13.84/2.27 sQ10_spl|sQ11_spl),
% 13.84/2.27 inference(split_clause,[status(thm)],[f176,f179,f182])).
% 13.84/2.27 fof(f193,plain,(
% 13.84/2.27 ~equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_identity)|~defined(multiplicative_inverse(a))),
% 13.84/2.27 inference(resolution,[status(thm)],[f102,f40])).
% 13.84/2.27 fof(f197,definition,(
% 13.84/2.27 sQ12_spl <=> (equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_identity))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f199,plain,(
% 13.84/2.27 ~equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_identity)|sQ12_spl),
% 13.84/2.27 inference(component_clause,[status(thm)],[f197])).
% 13.84/2.27 fof(f200,plain,(
% 13.84/2.27 ~sQ12_spl|~sQ10_spl),
% 13.84/2.27 inference(split_clause,[status(thm)],[f193,f197,f179])).
% 13.84/2.27 fof(f210,plain,(
% 13.84/2.27 ![X0]: (~equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),X0)|~equalish(X0,multiplicative_identity)|sQ12_spl)),
% 13.84/2.27 inference(resolution,[status(thm)],[f199,f66])).
% 13.84/2.27 fof(f326,plain,(
% 13.84/2.27 ~equalish(a,additive_identity)|~defined(a)|sQ3_spl),
% 13.84/2.27 inference(resolution,[status(thm)],[f160,f40])).
% 13.84/2.27 fof(f331,plain,(
% 13.84/2.27 ~sQ11_spl|~sQ4_spl|sQ3_spl),
% 13.84/2.27 inference(split_clause,[status(thm)],[f326,f182,f128,f125])).
% 13.84/2.27 fof(f1490,plain,(
% 13.84/2.27 ![X0]: (~equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)|~defined(multiplicative_inverse(a))|~equalish(multiplicative_identity,X0)|sQ12_spl)),
% 13.84/2.27 inference(resolution,[status(thm)],[f210,f70])).
% 13.84/2.27 fof(f1495,definition,(
% 13.84/2.27 ![X0]: (sQ213_spl <=> (~equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)|~equalish(multiplicative_identity,X0)))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f1496,plain,(
% 13.84/2.27 ![X0]: (~equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)|~equalish(multiplicative_identity,X0)|~sQ213_spl)),
% 13.84/2.27 inference(component_clause,[status(thm)],[f1495])).
% 13.84/2.27 fof(f1498,plain,(
% 13.84/2.27 sQ213_spl|~sQ10_spl|sQ12_spl),
% 13.84/2.27 inference(split_clause,[status(thm)],[f1490,f1495,f179,f197])).
% 13.84/2.27 fof(f7091,plain,(
% 13.84/2.27 ~equalish(multiplicative_identity,a)|~defined(a)|equalish(a,additive_identity)|~sQ213_spl),
% 13.84/2.27 inference(resolution,[status(thm)],[f1496,f41])).
% 13.84/2.27 fof(f7094,definition,(
% 13.84/2.27 sQ1250_spl <=> (equalish(multiplicative_identity,a))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ1250_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f7096,plain,(
% 13.84/2.27 ~equalish(multiplicative_identity,a)|sQ1250_spl),
% 13.84/2.27 inference(component_clause,[status(thm)],[f7094])).
% 13.84/2.27 fof(f7097,plain,(
% 13.84/2.27 ~sQ1250_spl|~sQ4_spl|sQ11_spl|~sQ213_spl),
% 13.84/2.30 inference(split_clause,[status(thm)],[f7091,f7094,f128,f182,f1495])).
% 13.84/2.30 fof(f7102,plain,(
% 13.84/2.30 ~equalish(a,multiplicative_identity)|sQ1250_spl),
% 13.84/2.30 inference(resolution,[status(thm)],[f7096,f64])).
% 13.84/2.30 fof(f7103,plain,(
% 13.84/2.30 $false|sQ1250_spl),
% 13.84/2.30 inference(forward_subsumption_resolution,[status(thm)],[f7102,f75])).
% 13.84/2.30 fof(f7104,plain,(
% 13.84/2.30 sQ1250_spl),
% 13.84/2.30 inference(contradiction_clause,[status(thm)],[f7103])).
% 13.84/2.30 fof(f7105,plain,(
% 13.84/2.30 $false),
% 13.84/2.30 inference(sat_refutation,[status(thm)],[f131,f137,f185,f200,f331,f1498,f7097,f7104])).
% 13.84/2.30 % SZS output end CNFRefutation for theBenchmark.p
% 0.99/2.34 % Elapsed time: 1.871861 seconds
% 0.99/2.34 % CPU time: 14.416764 seconds
% 0.99/2.34 % Total memory used: 180.480 MB
% 0.99/2.34 % Net memory used: 171.456 MB
%------------------------------------------------------------------------------