%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : FLD029-3 : 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 : n008.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 15.39s 2.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 15:39:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 15.39/2.38 % Refutation found
% 15.39/2.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 15.39/2.38 % SZS output start CNFRefutation for theBenchmark
% 15.39/2.38 fof(f1,axiom,(
% 15.39/2.38 (![X,V,W,Y,U,Z]: (( sum(X,V,W)| ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f2,axiom,(
% 15.39/2.38 (![U,Z,W,X,Y,V]: (( sum(U,Z,W)| ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(X,V,W) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f3,axiom,(
% 15.39/2.38 (![X]: (( sum(additive_identity,X,X)| ~ defined(X) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f4,axiom,(
% 15.39/2.38 (![X]: (( sum(additive_inverse(X),X,additive_identity)| ~ defined(X) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f5,axiom,(
% 15.39/2.38 (![Y,X,Z]: (( sum(Y,X,Z)| ~ sum(X,Y,Z) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f6,axiom,(
% 15.39/2.38 (![X,V,W,Y,U,Z]: (( product(X,V,W)| ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f7,axiom,(
% 15.39/2.38 (![U,Z,W,X,Y,V]: (( product(U,Z,W)| ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(X,V,W) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f8,axiom,(
% 15.39/2.38 (![X]: (( product(multiplicative_identity,X,X)| ~ defined(X) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f9,axiom,(
% 15.39/2.38 (![X]: (( product(multiplicative_inverse(X),X,multiplicative_identity)| sum(additive_identity,X,additive_identity)| ~ defined(X) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f11,axiom,(
% 15.39/2.38 (![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) ) ))),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f27,hypothesis,(
% 15.39/2.38 defined(a) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f28,hypothesis,(
% 15.39/2.38 defined(b) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f30,hypothesis,(
% 15.39/2.38 defined(v) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f31,negated_conjecture,(
% 15.39/2.38 ~ sum(additive_identity,b,additive_identity) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f32,negated_conjecture,(
% 15.39/2.38 product(a,u,b) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f33,negated_conjecture,(
% 15.39/2.38 product(a,v,b) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f34,negated_conjecture,(
% 15.39/2.38 ~ product(multiplicative_identity,u,v) ),
% 15.39/2.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.39/2.38 fof(f35,plain,(
% 15.39/2.38 ![W,U,Z]: ((![V,Y]: ((![X]: (sum(X,V,W)|~sum(X,Y,U)))|~sum(Y,Z,V)))|~sum(U,Z,W))),
% 15.39/2.38 inference(miniscoping,[status(thm)],[f1])).
% 15.39/2.38 fof(f36,plain,(
% 15.39/2.38 ![X0,X1,X2,X3,X4,X5]: (sum(X0,X1,X2)|~sum(X0,X3,X4)|~sum(X3,X5,X1)|~sum(X4,X5,X2))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f35])).
% 15.39/2.38 fof(f37,plain,(
% 15.39/2.38 ![W,X,V]: ((![Z,Y]: ((![U]: (sum(U,Z,W)|~sum(X,Y,U)))|~sum(Y,Z,V)))|~sum(X,V,W))),
% 15.39/2.38 inference(miniscoping,[status(thm)],[f2])).
% 15.39/2.38 fof(f38,plain,(
% 15.39/2.38 ![X0,X1,X2,X3,X4,X5]: (sum(X0,X1,X2)|~sum(X3,X4,X0)|~sum(X4,X1,X5)|~sum(X3,X5,X2))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f37])).
% 15.39/2.38 fof(f39,plain,(
% 15.39/2.38 ![X0]: (sum(additive_identity,X0,X0)|~defined(X0))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f3])).
% 15.39/2.38 fof(f40,plain,(
% 15.39/2.38 ![X0]: (sum(additive_inverse(X0),X0,additive_identity)|~defined(X0))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f4])).
% 15.39/2.38 fof(f41,plain,(
% 15.39/2.38 ![X0,X1,X2]: (sum(X0,X1,X2)|~sum(X1,X0,X2))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f5])).
% 15.39/2.38 fof(f42,plain,(
% 15.39/2.38 ![W,U,Z]: ((![V,Y]: ((![X]: (product(X,V,W)|~product(X,Y,U)))|~product(Y,Z,V)))|~product(U,Z,W))),
% 15.39/2.38 inference(miniscoping,[status(thm)],[f6])).
% 15.39/2.38 fof(f43,plain,(
% 15.39/2.38 ![X0,X1,X2,X3,X4,X5]: (product(X0,X1,X2)|~product(X0,X3,X4)|~product(X3,X5,X1)|~product(X4,X5,X2))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f42])).
% 15.39/2.38 fof(f44,plain,(
% 15.39/2.38 ![W,X,V]: ((![Z,Y]: ((![U]: (product(U,Z,W)|~product(X,Y,U)))|~product(Y,Z,V)))|~product(X,V,W))),
% 15.39/2.38 inference(miniscoping,[status(thm)],[f7])).
% 15.39/2.38 fof(f45,plain,(
% 15.39/2.38 ![X0,X1,X2,X3,X4,X5]: (product(X0,X1,X2)|~product(X3,X4,X0)|~product(X4,X1,X5)|~product(X3,X5,X2))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f44])).
% 15.39/2.38 fof(f46,plain,(
% 15.39/2.38 ![X0]: (product(multiplicative_identity,X0,X0)|~defined(X0))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f8])).
% 15.39/2.38 fof(f47,plain,(
% 15.39/2.38 ![X0]: (product(multiplicative_inverse(X0),X0,multiplicative_identity)|sum(additive_identity,X0,additive_identity)|~defined(X0))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f9])).
% 15.39/2.38 fof(f49,plain,(
% 15.39/2.38 ![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))),
% 15.39/2.38 inference(miniscoping,[status(thm)],[f11])).
% 15.39/2.38 fof(f50,plain,(
% 15.39/2.38 ![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))),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f49])).
% 15.39/2.38 fof(f74,plain,(
% 15.39/2.38 defined(a)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f27])).
% 15.39/2.38 fof(f75,plain,(
% 15.39/2.38 defined(b)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f28])).
% 15.39/2.38 fof(f77,plain,(
% 15.39/2.38 defined(v)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f30])).
% 15.39/2.38 fof(f78,plain,(
% 15.39/2.38 ~sum(additive_identity,b,additive_identity)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f31])).
% 15.39/2.38 fof(f79,plain,(
% 15.39/2.38 product(a,u,b)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f32])).
% 15.39/2.38 fof(f80,plain,(
% 15.39/2.38 product(a,v,b)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f33])).
% 15.39/2.38 fof(f81,plain,(
% 15.39/2.38 ~product(multiplicative_identity,u,v)),
% 15.39/2.38 inference(cnf_transformation,[status(thm)],[f34])).
% 15.39/2.38 fof(f84,plain,(
% 15.39/2.38 sum(additive_identity,a,a)),
% 15.39/2.38 inference(resolution,[status(thm)],[f39,f74])).
% 15.39/2.38 fof(f88,plain,(
% 15.39/2.38 sum(additive_inverse(b),b,additive_identity)),
% 15.39/2.38 inference(resolution,[status(thm)],[f40,f75])).
% 15.39/2.38 fof(f224,plain,(
% 15.39/2.38 product(multiplicative_inverse(a),a,multiplicative_identity)|sum(additive_identity,a,additive_identity)),
% 15.39/2.38 inference(resolution,[status(thm)],[f47,f74])).
% 15.39/2.38 fof(f237,definition,(
% 15.39/2.38 sQ28_spl <=> (sum(additive_identity,b,additive_identity))),
% 15.39/2.38 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 15.39/2.38 fof(f238,plain,(
% 15.39/2.38 sum(additive_identity,b,additive_identity)|~sQ28_spl),
% 15.39/2.38 inference(component_clause,[status(thm)],[f237])).
% 15.39/2.38 fof(f241,definition,(
% 15.39/2.38 sQ29_spl <=> (product(multiplicative_inverse(a),a,multiplicative_identity))),
% 15.39/2.38 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 15.39/2.38 fof(f242,plain,(
% 15.39/2.38 product(multiplicative_inverse(a),a,multiplicative_identity)|~sQ29_spl),
% 15.39/2.38 inference(component_clause,[status(thm)],[f241])).
% 15.39/2.38 fof(f244,definition,(
% 15.39/2.38 sQ30_spl <=> (sum(additive_identity,a,additive_identity))),
% 15.39/2.38 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 15.39/2.38 fof(f245,plain,(
% 15.39/2.38 sum(additive_identity,a,additive_identity)|~sQ30_spl),
% 15.39/2.38 inference(component_clause,[status(thm)],[f244])).
% 15.39/2.38 fof(f247,plain,(
% 15.39/2.38 sQ29_spl|sQ30_spl),
% 15.39/2.38 inference(split_clause,[status(thm)],[f224,f241,f244])).
% 15.39/2.38 fof(f287,plain,(
% 15.39/2.38 $false|~sQ28_spl),
% 15.39/2.38 inference(forward_subsumption_resolution,[status(thm)],[f238,f78])).
% 15.39/2.38 fof(f288,plain,(
% 15.39/2.38 ~sQ28_spl),
% 15.39/2.38 inference(contradiction_clause,[status(thm)],[f287])).
% 15.39/2.38 fof(f361,plain,(
% 15.39/2.38 ![X0,X1,X2]: (product(X0,b,X1)|~product(X0,a,X2)|~product(X2,v,X1))),
% 15.39/2.38 inference(resolution,[status(thm)],[f43,f80])).
% 15.39/2.38 fof(f371,plain,(
% 15.39/2.38 ![X0,X1,X2]: (product(X0,u,X1)|~product(X2,a,X0)|~product(X2,b,X1))),
% 15.39/2.38 inference(resolution,[status(thm)],[f45,f79])).
% 15.39/2.38 fof(f378,plain,(
% 15.39/2.38 product(multiplicative_identity,v,v)),
% 15.39/2.38 inference(resolution,[status(thm)],[f46,f77])).
% 15.39/2.38 fof(f413,plain,(
% 15.39/2.38 sum(b,b,b)|~sum(a,a,a)),
% 15.39/2.38 inference(resolution,[status(thm)],[f50,f80])).
% 15.39/2.38 fof(f429,definition,(
% 15.39/2.38 sQ54_spl <=> (sum(b,b,b))),
% 15.39/2.38 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 15.39/2.38 fof(f430,plain,(
% 15.39/2.38 sum(b,b,b)|~sQ54_spl),
% 15.39/2.38 inference(component_clause,[status(thm)],[f429])).
% 15.39/2.38 fof(f440,definition,(
% 15.39/2.38 sQ57_spl <=> (sum(a,a,a))),
% 15.39/2.38 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 15.39/2.38 fof(f442,plain,(
% 15.39/2.38 ~sum(a,a,a)|sQ57_spl),
% 15.39/2.38 inference(component_clause,[status(thm)],[f440])).
% 15.39/2.38 fof(f443,plain,(
% 15.39/2.41 sQ54_spl|~sQ57_spl),
% 15.39/2.41 inference(split_clause,[status(thm)],[f413,f429,f440])).
% 15.39/2.41 fof(f480,plain,(
% 15.39/2.41 ![X0,X1,X2]: (sum(X0,b,X1)|~sum(X2,b,X0)|~sum(X2,b,X1)|~sQ54_spl)),
% 15.39/2.41 inference(resolution,[status(thm)],[f430,f38])).
% 15.39/2.41 fof(f1352,plain,(
% 15.39/2.41 ![X0]: (sum(X0,a,a)|~sum(X0,additive_identity,additive_identity))),
% 15.39/2.41 inference(resolution,[status(thm)],[f84,f36])).
% 15.39/2.41 fof(f1389,plain,(
% 15.39/2.41 ![X0]: (sum(X0,b,additive_identity)|~sum(additive_inverse(b),b,X0)|~sQ54_spl)),
% 15.39/2.41 inference(resolution,[status(thm)],[f88,f480])).
% 15.39/2.41 fof(f1398,plain,(
% 15.39/2.41 sum(additive_identity,b,additive_identity)|~sQ54_spl),
% 15.39/2.41 inference(resolution,[status(thm)],[f1389,f88])).
% 15.39/2.41 fof(f1399,plain,(
% 15.39/2.41 sQ28_spl|~sQ54_spl),
% 15.39/2.41 inference(split_clause,[status(thm)],[f1398,f237,f429])).
% 15.39/2.41 fof(f1645,plain,(
% 15.39/2.41 sum(a,additive_identity,additive_identity)|~sQ30_spl),
% 15.39/2.41 inference(resolution,[status(thm)],[f245,f41])).
% 15.39/2.41 fof(f1871,plain,(
% 15.39/2.41 ![X0]: (product(X0,b,v)|~product(X0,a,multiplicative_identity))),
% 15.39/2.41 inference(resolution,[status(thm)],[f378,f361])).
% 15.39/2.41 fof(f6523,plain,(
% 15.39/2.41 sum(a,a,a)|~sQ30_spl),
% 15.39/2.41 inference(resolution,[status(thm)],[f1645,f1352])).
% 15.39/2.41 fof(f6537,plain,(
% 15.39/2.41 $false|sQ57_spl|~sQ30_spl),
% 15.39/2.41 inference(forward_subsumption_resolution,[status(thm)],[f6523,f442])).
% 15.39/2.41 fof(f6538,plain,(
% 15.39/2.41 sQ57_spl|~sQ30_spl),
% 15.39/2.41 inference(contradiction_clause,[status(thm)],[f6537])).
% 15.39/2.41 fof(f6956,plain,(
% 15.39/2.41 product(multiplicative_inverse(a),b,v)|~sQ29_spl),
% 15.39/2.41 inference(resolution,[status(thm)],[f242,f1871])).
% 15.39/2.41 fof(f7641,plain,(
% 15.39/2.41 ![X0]: (product(X0,u,v)|~product(multiplicative_inverse(a),a,X0)|~sQ29_spl)),
% 15.39/2.41 inference(resolution,[status(thm)],[f6956,f371])).
% 15.39/2.41 fof(f8739,plain,(
% 15.39/2.41 product(multiplicative_identity,u,v)|~sQ29_spl),
% 15.39/2.41 inference(resolution,[status(thm)],[f7641,f242])).
% 15.39/2.41 fof(f8740,plain,(
% 15.39/2.41 $false|~sQ29_spl),
% 15.39/2.41 inference(forward_subsumption_resolution,[status(thm)],[f8739,f81])).
% 15.39/2.41 fof(f8741,plain,(
% 15.39/2.41 ~sQ29_spl),
% 15.39/2.41 inference(contradiction_clause,[status(thm)],[f8740])).
% 15.39/2.41 fof(f8742,plain,(
% 15.39/2.41 $false),
% 15.39/2.41 inference(sat_refutation,[status(thm)],[f247,f288,f443,f1399,f6538,f8741])).
% 15.39/2.41 % SZS output end CNFRefutation for theBenchmark.p
% 15.39/2.44 % Elapsed time: 2.051199 seconds
% 15.39/2.44 % CPU time: 15.890716 seconds
% 15.39/2.44 % Total memory used: 161.258 MB
% 15.39/2.44 % Net memory used: 152.574 MB
%------------------------------------------------------------------------------