%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : FLD040-5 : 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 : n011.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 0.12s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD040-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 15:39:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.12/0.52 % Refutation found
% 0.12/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.52 fof(f1,axiom,(
% 0.12/0.52 (![X,V,W,Y,U,Z]: (( sum(X,V,W)| ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f2,axiom,(
% 0.12/0.52 (![U,Z,W,X,Y,V]: (( sum(U,Z,W)| ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(X,V,W) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f3,axiom,(
% 0.12/0.52 (![X]: (( sum(additive_identity,X,X)| ~ defined(X) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f4,axiom,(
% 0.12/0.52 (![X]: (( sum(additive_inverse(X),X,additive_identity)| ~ defined(X) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f5,axiom,(
% 0.12/0.52 (![Y,X,Z]: (( sum(Y,X,Z)| ~ sum(X,Y,Z) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f8,axiom,(
% 0.12/0.52 (![X]: (( product(multiplicative_identity,X,X)| ~ defined(X) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f9,axiom,(
% 0.12/0.52 (![X]: (( product(multiplicative_inverse(X),X,multiplicative_identity)| sum(additive_identity,X,additive_identity)| ~ defined(X) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f11,axiom,(
% 0.12/0.52 (![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) ) ))),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f17,axiom,(
% 0.12/0.52 defined(multiplicative_identity) ),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f26,axiom,(
% 0.12/0.52 ~ sum(additive_identity,additive_identity,multiplicative_identity) ),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f27,hypothesis,(
% 0.12/0.52 defined(a) ),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f28,negated_conjecture,(
% 0.12/0.52 ~ sum(additive_identity,a,additive_identity) ),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f29,negated_conjecture,(
% 0.12/0.52 sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
% 0.12/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.52 fof(f30,plain,(
% 0.12/0.52 ![W,U,Z]: ((![V,Y]: ((![X]: (sum(X,V,W)|~sum(X,Y,U)))|~sum(Y,Z,V)))|~sum(U,Z,W))),
% 0.12/0.52 inference(miniscoping,[status(thm)],[f1])).
% 0.12/0.52 fof(f31,plain,(
% 0.12/0.52 ![X0,X1,X2,X3,X4,X5]: (sum(X0,X1,X2)|~sum(X0,X3,X4)|~sum(X3,X5,X1)|~sum(X4,X5,X2))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f30])).
% 0.12/0.52 fof(f32,plain,(
% 0.12/0.52 ![W,X,V]: ((![Z,Y]: ((![U]: (sum(U,Z,W)|~sum(X,Y,U)))|~sum(Y,Z,V)))|~sum(X,V,W))),
% 0.12/0.52 inference(miniscoping,[status(thm)],[f2])).
% 0.12/0.52 fof(f33,plain,(
% 0.12/0.52 ![X0,X1,X2,X3,X4,X5]: (sum(X0,X1,X2)|~sum(X3,X4,X0)|~sum(X4,X1,X5)|~sum(X3,X5,X2))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f32])).
% 0.12/0.52 fof(f34,plain,(
% 0.12/0.52 ![X0]: (sum(additive_identity,X0,X0)|~defined(X0))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.52 fof(f35,plain,(
% 0.12/0.52 ![X0]: (sum(additive_inverse(X0),X0,additive_identity)|~defined(X0))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.52 fof(f36,plain,(
% 0.12/0.52 ![X0,X1,X2]: (sum(X0,X1,X2)|~sum(X1,X0,X2))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.52 fof(f41,plain,(
% 0.12/0.52 ![X0]: (product(multiplicative_identity,X0,X0)|~defined(X0))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.52 fof(f42,plain,(
% 0.12/0.52 ![X0]: (product(multiplicative_inverse(X0),X0,multiplicative_identity)|sum(additive_identity,X0,additive_identity)|~defined(X0))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.52 fof(f44,plain,(
% 0.12/0.52 ![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))),
% 0.12/0.52 inference(miniscoping,[status(thm)],[f11])).
% 0.12/0.52 fof(f45,plain,(
% 0.12/0.52 ![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))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f44])).
% 0.12/0.52 fof(f54,plain,(
% 0.12/0.52 defined(multiplicative_identity)),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.52 fof(f68,plain,(
% 0.12/0.52 ~sum(additive_identity,additive_identity,multiplicative_identity)),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f26])).
% 0.12/0.52 fof(f69,plain,(
% 0.12/0.52 defined(a)),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.12/0.53 fof(f70,plain,(
% 0.12/0.53 ~sum(additive_identity,a,additive_identity)),
% 0.12/0.53 inference(cnf_transformation,[status(thm)],[f28])).
% 0.12/0.53 fof(f71,plain,(
% 0.12/0.53 sum(additive_identity,multiplicative_inverse(a),additive_identity)),
% 0.12/0.53 inference(cnf_transformation,[status(thm)],[f29])).
% 0.12/0.53 fof(f75,plain,(
% 0.12/0.53 sum(additive_identity,a,a)),
% 0.12/0.53 inference(resolution,[status(thm)],[f34,f69])).
% 0.12/0.53 fof(f83,plain,(
% 0.12/0.53 ![X0,X1,X2]: (sum(X0,multiplicative_inverse(a),X1)|~sum(X2,additive_identity,X0)|~sum(X2,additive_identity,X1))),
% 0.12/0.53 inference(resolution,[status(thm)],[f33,f71])).
% 0.12/0.53 fof(f86,plain,(
% 0.12/0.53 sum(a,additive_identity,a)),
% 0.12/0.53 inference(resolution,[status(thm)],[f36,f75])).
% 0.12/0.53 fof(f88,plain,(
% 0.12/0.53 sum(additive_identity,multiplicative_identity,multiplicative_identity)),
% 0.12/0.53 inference(resolution,[status(thm)],[f54,f34])).
% 0.12/0.53 fof(f102,plain,(
% 0.12/0.53 sum(additive_inverse(a),a,additive_identity)),
% 0.12/0.53 inference(resolution,[status(thm)],[f35,f69])).
% 0.12/0.53 fof(f134,definition,(
% 0.12/0.53 sQ7_spl <=> (sum(additive_identity,multiplicative_identity,additive_identity))),
% 0.12/0.53 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.53 fof(f135,plain,(
% 0.12/0.53 sum(additive_identity,multiplicative_identity,additive_identity)|~sQ7_spl),
% 0.12/0.53 inference(component_clause,[status(thm)],[f134])).
% 0.12/0.53 fof(f141,definition,(
% 0.12/0.53 sQ9_spl <=> (sum(additive_identity,a,additive_identity))),
% 0.12/0.53 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.53 fof(f142,plain,(
% 0.12/0.53 sum(additive_identity,a,additive_identity)|~sQ9_spl),
% 0.12/0.53 inference(component_clause,[status(thm)],[f141])).
% 0.12/0.53 fof(f156,plain,(
% 0.12/0.53 product(multiplicative_inverse(a),a,multiplicative_identity)|sum(additive_identity,a,additive_identity)),
% 0.12/0.53 inference(resolution,[status(thm)],[f42,f69])).
% 0.12/0.53 fof(f174,definition,(
% 0.12/0.53 sQ16_spl <=> (product(multiplicative_inverse(a),a,multiplicative_identity))),
% 0.12/0.53 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.12/0.53 fof(f175,plain,(
% 0.12/0.53 product(multiplicative_inverse(a),a,multiplicative_identity)|~sQ16_spl),
% 0.12/0.53 inference(component_clause,[status(thm)],[f174])).
% 0.12/0.53 fof(f177,plain,(
% 0.12/0.53 sQ16_spl|sQ9_spl),
% 0.12/0.53 inference(split_clause,[status(thm)],[f156,f174,f141])).
% 0.12/0.53 fof(f182,plain,(
% 0.12/0.53 $false|~sQ9_spl),
% 0.12/0.53 inference(forward_subsumption_resolution,[status(thm)],[f142,f70])).
% 0.12/0.53 fof(f183,plain,(
% 0.12/0.53 ~sQ9_spl),
% 0.12/0.53 inference(contradiction_clause,[status(thm)],[f182])).
% 0.12/0.53 fof(f479,plain,(
% 0.12/0.53 sum(multiplicative_identity,additive_identity,multiplicative_identity)),
% 0.12/0.53 inference(resolution,[status(thm)],[f88,f36])).
% 0.12/0.53 fof(f513,plain,(
% 0.12/0.53 ![X0]: (sum(X0,multiplicative_inverse(a),a)|~sum(a,additive_identity,X0))),
% 0.12/0.53 inference(resolution,[status(thm)],[f86,f83])).
% 0.12/0.53 fof(f521,plain,(
% 0.12/0.53 sum(a,multiplicative_inverse(a),a)),
% 0.12/0.53 inference(resolution,[status(thm)],[f513,f86])).
% 0.12/0.53 fof(f528,plain,(
% 0.12/0.53 ![X0,X1,X2]: (sum(X0,multiplicative_inverse(a),X1)|~sum(X2,a,X0)|~sum(X2,a,X1))),
% 0.12/0.53 inference(resolution,[status(thm)],[f521,f33])).
% 0.12/0.53 fof(f543,plain,(
% 0.12/0.53 ![X0]: (sum(X0,multiplicative_inverse(a),additive_identity)|~sum(additive_inverse(a),a,X0))),
% 0.12/0.53 inference(resolution,[status(thm)],[f528,f102])).
% 0.12/0.53 fof(f910,plain,(
% 0.12/0.53 product(multiplicative_identity,a,a)),
% 0.12/0.53 inference(resolution,[status(thm)],[f41,f69])).
% 0.12/0.53 fof(f1105,plain,(
% 0.12/0.53 ![X0]: (sum(X0,multiplicative_inverse(a),multiplicative_identity)|~sum(multiplicative_identity,additive_identity,X0))),
% 0.12/0.53 inference(resolution,[status(thm)],[f479,f83])).
% 0.12/0.53 fof(f1114,plain,(
% 0.12/0.53 sum(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1105,f479])).
% 0.12/0.53 fof(f1123,plain,(
% 0.12/0.53 ![X0,X1,X2,X3]: (sum(X0,X1,X2)|~product(multiplicative_identity,X3,X2)|~product(multiplicative_identity,X3,X0)|~product(multiplicative_inverse(a),X3,X1))),
% 0.12/0.53 inference(resolution,[status(thm)],[f1114,f45])).
% 0.12/0.53 fof(f1126,plain,(
% 0.12/0.53 ![X0,X1,X2]: (sum(X0,multiplicative_inverse(a),X1)|~sum(X2,multiplicative_identity,X0)|~sum(X2,multiplicative_identity,X1))),
% 0.12/0.53 inference(resolution,[status(thm)],[f1114,f33])).
% 0.12/0.53 fof(f1128,plain,(
% 0.12/0.53 ![X0,X1,X2]: (sum(X0,X1,multiplicative_identity)|~sum(X0,X2,multiplicative_identity)|~sum(X2,multiplicative_inverse(a),X1))),
% 0.12/0.53 inference(resolution,[status(thm)],[f1114,f31])).
% 0.12/0.53 fof(f1130,plain,(
% 0.12/0.53 ![X0,X1,X2]: (sum(X0,multiplicative_identity,X1)|~sum(X0,multiplicative_identity,X2)|~sum(X2,multiplicative_inverse(a),X1))),
% 0.12/0.53 inference(resolution,[status(thm)],[f1114,f31])).
% 0.12/0.53 fof(f1144,plain,(
% 0.12/0.53 ![X0]: (sum(X0,multiplicative_inverse(a),additive_identity)|~sum(additive_identity,multiplicative_identity,X0)|~sQ7_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1126,f135])).
% 0.12/0.53 fof(f1147,plain,(
% 0.12/0.53 sum(multiplicative_identity,multiplicative_inverse(a),additive_identity)|~sQ7_spl),
% 0.12/0.53 inference(resolution,[status(thm)],[f1144,f88])).
% 0.12/0.53 fof(f1148,plain,(
% 0.12/0.53 ![X0,X1]: (sum(X0,multiplicative_identity,X1)|~product(multiplicative_identity,a,X1)|~product(multiplicative_identity,a,X0)|~sQ16_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1123,f175])).
% 0.12/0.53 fof(f1169,plain,(
% 0.12/0.53 ![X0]: (sum(X0,additive_identity,multiplicative_identity)|~sum(X0,multiplicative_identity,multiplicative_identity)|~sQ7_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1147,f1128])).
% 0.12/0.53 fof(f1248,plain,(
% 0.12/0.53 sum(additive_identity,additive_identity,multiplicative_identity)|~sQ7_spl),
% 0.12/0.53 inference(resolution,[status(thm)],[f1169,f88])).
% 0.12/0.53 fof(f1249,plain,(
% 0.12/0.53 $false|~sQ7_spl),
% 0.12/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1248,f68])).
% 0.12/0.53 fof(f1250,plain,(
% 0.12/0.53 ~sQ7_spl),
% 0.12/0.53 inference(contradiction_clause,[status(thm)],[f1249])).
% 0.12/0.53 fof(f1253,plain,(
% 0.12/0.53 ![X0]: (sum(X0,multiplicative_identity,a)|~product(multiplicative_identity,a,X0)|~sQ16_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1148,f910])).
% 0.12/0.53 fof(f1254,plain,(
% 0.12/0.53 sum(a,multiplicative_identity,a)|~sQ16_spl),
% 0.12/0.53 inference(resolution,[status(thm)],[f1253,f910])).
% 0.12/0.53 fof(f1263,plain,(
% 0.12/0.53 ![X0,X1,X2]: (sum(X0,a,X1)|~sum(X0,a,X2)|~sum(X2,multiplicative_identity,X1)|~sQ16_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1254,f31])).
% 0.12/0.53 fof(f1296,plain,(
% 0.12/0.53 ![X0]: (sum(X0,a,multiplicative_identity)|~sum(X0,a,additive_identity)|~sQ16_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1263,f88])).
% 0.12/0.53 fof(f1723,plain,(
% 0.12/0.53 sum(additive_inverse(a),a,multiplicative_identity)|~sQ16_spl),
% 0.12/0.53 inference(resolution,[status(thm)],[f1296,f102])).
% 0.12/0.53 fof(f1724,plain,(
% 0.12/0.53 sum(multiplicative_identity,multiplicative_inverse(a),additive_identity)|~sQ16_spl),
% 0.12/0.53 inference(resolution,[status(thm)],[f1723,f543])).
% 0.12/0.53 fof(f1742,plain,(
% 0.12/0.53 ![X0]: (sum(X0,multiplicative_identity,additive_identity)|~sum(X0,multiplicative_identity,multiplicative_identity)|~sQ16_spl)),
% 0.12/0.53 inference(resolution,[status(thm)],[f1724,f1130])).
% 0.12/0.53 fof(f1859,plain,(
% 0.12/0.53 sum(additive_identity,multiplicative_identity,additive_identity)|~sQ16_spl),
% 0.12/0.53 inference(resolution,[status(thm)],[f1742,f88])).
% 0.12/0.53 fof(f1860,plain,(
% 0.12/0.53 sQ7_spl|~sQ16_spl),
% 0.12/0.53 inference(split_clause,[status(thm)],[f1859,f134,f174])).
% 0.12/0.53 fof(f1861,plain,(
% 0.12/0.53 $false),
% 0.12/0.53 inference(sat_refutation,[status(thm)],[f177,f183,f1250,f1860])).
% 0.12/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.55 % Elapsed time: 0.172380 seconds
% 0.16/0.55 % CPU time: 1.195487 seconds
% 0.16/0.55 % Total memory used: 34.654 MB
% 0.16/0.55 % Net memory used: 33.455 MB
%------------------------------------------------------------------------------