%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO331+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:26:22 PM UTC 2026
% Result : Theorem 0.60s 0.64s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO331+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.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 : Sun Sep 20 15:26:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % Drodi V4.1.1
% 0.60/0.64 % Refutation found
% 0.60/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.60/0.64 % SZS output start CNFRefutation for theBenchmark
% 0.60/0.64 fof(f1,conjecture,(
% 0.60/0.64 vf(vd1352,vd1353) = vf(vd1352,vd1354) ),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f2,negated_conjecture,(
% 0.60/0.64 ~(vf(vd1352,vd1353) = vf(vd1352,vd1354) )),
% 0.60/0.64 inference(negated_conjecture,[status(cth)],[f1])).
% 0.60/0.64 fof(f3,axiom,(
% 0.60/0.64 vangle(vd1352,vd1353,vd1354) = vangle(vd1352,vd1354,vd1353) ),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f4,axiom,(
% 0.60/0.64 vd1353 != vd1354 ),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f5,axiom,(
% 0.60/0.64 vd1352 != vd1354 ),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f6,axiom,(
% 0.60/0.64 vd1352 != vd1353 ),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f7,axiom,(
% 0.60/0.64 (? [Vd1359] :( vd1354 = Vd1359& rpoint(Vd1359) ) )),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f8,axiom,(
% 0.60/0.64 (? [Vd1358] :( vd1353 = Vd1358& rpoint(Vd1358) ) )),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f9,axiom,(
% 0.60/0.64 (? [Vd1357] :( vd1352 = Vd1357& rpoint(Vd1357) ) )),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f10,axiom,(
% 0.60/0.64 (! [Vd1361,Vd1362,Vd1363] :( ( vangle(Vd1361,Vd1362,Vd1363) = vangle(Vd1361,Vd1363,Vd1362)& Vd1362 != Vd1363& Vd1361 != Vd1363& Vd1361 != Vd1362& (? [Vd1368] :( Vd1363 = Vd1368& rpoint(Vd1368) ))& (? [Vd1367] :( Vd1362 = Vd1367& rpoint(Vd1367) ))& (? [Vd1366] :( Vd1361 = Vd1366& rpoint(Vd1366) ) ))=> ( vf(Vd1361,Vd1362) != vf(Vd1361,Vd1363)=> ( rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363))| rless(vf(Vd1361,Vd1363),vf(Vd1361,Vd1362)) ) ) ) )),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f11,axiom,(
% 0.60/0.64 (! [Vd1361,Vd1362,Vd1363] :( ( vangle(Vd1361,Vd1362,Vd1363) = vangle(Vd1361,Vd1363,Vd1362)& Vd1362 != Vd1363& Vd1361 != Vd1363& Vd1361 != Vd1362& (? [Vd1368] :( Vd1363 = Vd1368& rpoint(Vd1368) ))& (? [Vd1367] :( Vd1362 = Vd1367& rpoint(Vd1367) ))& (? [Vd1366] :( Vd1361 = Vd1366& rpoint(Vd1366) ) ))=> ( vf(Vd1361,Vd1362) != vf(Vd1361,Vd1363)=> ~ rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363)) ) ) )),
% 0.60/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.60/0.64 fof(f128,plain,(
% 0.60/0.64 ~vf(vd1352,vd1353)=vf(vd1352,vd1354)),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f2])).
% 0.60/0.64 fof(f129,plain,(
% 0.60/0.64 vangle(vd1352,vd1353,vd1354)=vangle(vd1352,vd1354,vd1353)),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f3])).
% 0.60/0.64 fof(f130,plain,(
% 0.60/0.64 ~vd1353=vd1354),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f4])).
% 0.60/0.64 fof(f131,plain,(
% 0.60/0.64 ~vd1352=vd1354),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f5])).
% 0.60/0.64 fof(f132,plain,(
% 0.60/0.64 ~vd1352=vd1353),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f6])).
% 0.60/0.64 fof(f133,plain,(
% 0.60/0.64 (vd1354=sK0_skl&rpoint(sK0_skl))),
% 0.60/0.64 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd1359,sK0_skl)],[f7])).
% 0.60/0.64 fof(f134,plain,(
% 0.60/0.64 vd1354=sK0_skl),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f133])).
% 0.60/0.64 fof(f135,plain,(
% 0.60/0.64 rpoint(sK0_skl)),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f133])).
% 0.60/0.64 fof(f136,plain,(
% 0.60/0.64 (vd1353=sK1_skl&rpoint(sK1_skl))),
% 0.60/0.64 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Vd1358,sK1_skl)],[f8])).
% 0.60/0.64 fof(f137,plain,(
% 0.60/0.64 vd1353=sK1_skl),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f136])).
% 0.60/0.64 fof(f138,plain,(
% 0.60/0.64 rpoint(sK1_skl)),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f136])).
% 0.60/0.64 fof(f139,plain,(
% 0.60/0.64 (vd1352=sK2_skl&rpoint(sK2_skl))),
% 0.60/0.64 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Vd1357,sK2_skl)],[f9])).
% 0.60/0.64 fof(f140,plain,(
% 0.60/0.64 vd1352=sK2_skl),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f139])).
% 0.60/0.64 fof(f141,plain,(
% 0.60/0.64 rpoint(sK2_skl)),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f139])).
% 0.60/0.64 fof(f142,plain,(
% 0.60/0.64 ![Vd1361,Vd1362,Vd1363]: (((((((~vangle(Vd1361,Vd1362,Vd1363)=vangle(Vd1361,Vd1363,Vd1362)|Vd1362=Vd1363)|Vd1361=Vd1363)|Vd1361=Vd1362)|(![Vd1368]: (~Vd1363=Vd1368|~rpoint(Vd1368))))|(![Vd1367]: (~Vd1362=Vd1367|~rpoint(Vd1367))))|(![Vd1366]: (~Vd1361=Vd1366|~rpoint(Vd1366))))|(vf(Vd1361,Vd1362)=vf(Vd1361,Vd1363)|(rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363))|rless(vf(Vd1361,Vd1363),vf(Vd1361,Vd1362)))))),
% 0.60/0.64 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.60/0.64 fof(f143,plain,(
% 0.60/0.64 ![X0,X1,X2,X3,X4,X5]: (~vangle(X0,X1,X2)=vangle(X0,X2,X1)|X1=X2|X0=X2|X0=X1|~X2=X3|~rpoint(X3)|~X1=X4|~rpoint(X4)|~X0=X5|~rpoint(X5)|vf(X0,X1)=vf(X0,X2)|rless(vf(X0,X1),vf(X0,X2))|rless(vf(X0,X2),vf(X0,X1)))),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f142])).
% 0.60/0.64 fof(f144,plain,(
% 0.60/0.64 ![Vd1361,Vd1362,Vd1363]: (((((((~vangle(Vd1361,Vd1362,Vd1363)=vangle(Vd1361,Vd1363,Vd1362)|Vd1362=Vd1363)|Vd1361=Vd1363)|Vd1361=Vd1362)|(![Vd1368]: (~Vd1363=Vd1368|~rpoint(Vd1368))))|(![Vd1367]: (~Vd1362=Vd1367|~rpoint(Vd1367))))|(![Vd1366]: (~Vd1361=Vd1366|~rpoint(Vd1366))))|(vf(Vd1361,Vd1362)=vf(Vd1361,Vd1363)|~rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363))))),
% 0.60/0.64 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.60/0.64 fof(f145,plain,(
% 0.60/0.64 ![X0,X1,X2,X3,X4,X5]: (~vangle(X0,X1,X2)=vangle(X0,X2,X1)|X1=X2|X0=X2|X0=X1|~X2=X3|~rpoint(X3)|~X1=X4|~rpoint(X4)|~X0=X5|~rpoint(X5)|vf(X0,X1)=vf(X0,X2)|~rless(vf(X0,X1),vf(X0,X2)))),
% 0.60/0.64 inference(cnf_transformation,[status(thm)],[f144])).
% 0.60/0.64 fof(f703,plain,(
% 0.60/0.64 ![X0,X1,X2]: (~vangle(X0,X1,X2)=vangle(X0,X2,X1)|X1=X2|X0=X2|X0=X1|~rpoint(X2)|~rpoint(X1)|~rpoint(X0)|vf(X0,X1)=vf(X0,X2)|rless(vf(X0,X1),vf(X0,X2))|rless(vf(X0,X2),vf(X0,X1)))),
% 0.60/0.64 inference(destructive_equality_resolution,[status(thm)],[f143])).
% 0.60/0.64 fof(f704,plain,(
% 0.60/0.64 ![X0,X1,X2]: (~vangle(X0,X1,X2)=vangle(X0,X2,X1)|X1=X2|X0=X2|X0=X1|~rpoint(X2)|~rpoint(X1)|~rpoint(X0)|vf(X0,X1)=vf(X0,X2)|~rless(vf(X0,X1),vf(X0,X2)))),
% 0.60/0.64 inference(destructive_equality_resolution,[status(thm)],[f145])).
% 0.60/0.64 fof(f941,plain,(
% 0.60/0.64 rpoint(vd1354)),
% 0.60/0.64 inference(forward_demodulation,[status(thm)],[f134,f135])).
% 0.60/0.64 fof(f944,plain,(
% 0.60/0.64 rpoint(vd1353)),
% 0.60/0.64 inference(forward_demodulation,[status(thm)],[f137,f138])).
% 0.60/0.64 fof(f949,plain,(
% 0.60/0.64 rpoint(vd1352)),
% 0.60/0.64 inference(forward_demodulation,[status(thm)],[f140,f141])).
% 0.60/0.64 fof(f974,plain,(
% 0.60/0.64 vd1353=vd1354|vd1352=vd1354|vd1352=vd1353|~rpoint(vd1354)|~rpoint(vd1353)|~rpoint(vd1352)|vf(vd1352,vd1353)=vf(vd1352,vd1354)|rless(vf(vd1352,vd1353),vf(vd1352,vd1354))|rless(vf(vd1352,vd1354),vf(vd1352,vd1353))),
% 0.60/0.64 inference(resolution,[status(thm)],[f703,f129])).
% 0.60/0.64 fof(f979,definition,(
% 0.60/0.64 sQ8_spl <=> (vd1353=vd1354)),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f980,plain,(
% 0.60/0.64 vd1353=vd1354|~sQ8_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f979])).
% 0.60/0.64 fof(f982,definition,(
% 0.60/0.64 sQ9_spl <=> (vd1352=vd1354)),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f983,plain,(
% 0.60/0.64 vd1352=vd1354|~sQ9_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f982])).
% 0.60/0.64 fof(f985,definition,(
% 0.60/0.64 sQ10_spl <=> (vd1352=vd1353)),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f986,plain,(
% 0.60/0.64 vd1352=vd1353|~sQ10_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f985])).
% 0.60/0.64 fof(f988,definition,(
% 0.60/0.64 sQ11_spl <=> (rpoint(vd1354))),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f990,plain,(
% 0.60/0.64 ~rpoint(vd1354)|sQ11_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f988])).
% 0.60/0.64 fof(f991,definition,(
% 0.60/0.64 sQ12_spl <=> (rpoint(vd1353))),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f993,plain,(
% 0.60/0.64 ~rpoint(vd1353)|sQ12_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f991])).
% 0.60/0.64 fof(f994,definition,(
% 0.60/0.64 sQ13_spl <=> (rpoint(vd1352))),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f996,plain,(
% 0.60/0.64 ~rpoint(vd1352)|sQ13_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f994])).
% 0.60/0.64 fof(f997,definition,(
% 0.60/0.64 sQ14_spl <=> (vf(vd1352,vd1353)=vf(vd1352,vd1354))),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.60/0.64 fof(f998,plain,(
% 0.60/0.64 vf(vd1352,vd1353)=vf(vd1352,vd1354)|~sQ14_spl),
% 0.60/0.64 inference(component_clause,[status(thm)],[f997])).
% 0.60/0.64 fof(f1000,definition,(
% 0.60/0.64 sQ15_spl <=> (rless(vf(vd1352,vd1353),vf(vd1352,vd1354)))),
% 0.60/0.64 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.60/0.65 fof(f1003,definition,(
% 0.60/0.65 sQ16_spl <=> (rless(vf(vd1352,vd1354),vf(vd1352,vd1353)))),
% 0.60/0.65 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.60/0.65 fof(f1006,plain,(
% 0.60/0.65 sQ8_spl|sQ9_spl|sQ10_spl|~sQ11_spl|~sQ12_spl|~sQ13_spl|sQ14_spl|sQ15_spl|sQ16_spl),
% 0.60/0.65 inference(split_clause,[status(thm)],[f974,f979,f982,f985,f988,f991,f994,f997,f1000,f1003])).
% 0.60/0.65 fof(f1014,plain,(
% 0.60/0.65 vd1353=vd1354|vd1352=vd1354|vd1352=vd1353|~rpoint(vd1354)|~rpoint(vd1353)|~rpoint(vd1352)|vf(vd1352,vd1353)=vf(vd1352,vd1354)|~rless(vf(vd1352,vd1353),vf(vd1352,vd1354))),
% 0.60/0.65 inference(resolution,[status(thm)],[f704,f129])).
% 0.60/0.65 fof(f1015,plain,(
% 0.60/0.65 vd1354=vd1353|vd1352=vd1353|vd1352=vd1354|~rpoint(vd1353)|~rpoint(vd1354)|~rpoint(vd1352)|vf(vd1352,vd1354)=vf(vd1352,vd1353)|~rless(vf(vd1352,vd1354),vf(vd1352,vd1353))),
% 0.60/0.65 inference(resolution,[status(thm)],[f704,f129])).
% 0.60/0.65 fof(f1020,plain,(
% 0.60/0.65 sQ8_spl|sQ9_spl|sQ10_spl|~sQ11_spl|~sQ12_spl|~sQ13_spl|sQ14_spl|~sQ15_spl),
% 0.60/0.65 inference(split_clause,[status(thm)],[f1014,f979,f982,f985,f988,f991,f994,f997,f1000])).
% 0.60/0.65 fof(f1021,plain,(
% 0.60/0.65 sQ8_spl|sQ10_spl|sQ9_spl|~sQ12_spl|~sQ11_spl|~sQ13_spl|sQ14_spl|~sQ16_spl),
% 0.60/0.65 inference(split_clause,[status(thm)],[f1015,f979,f985,f982,f991,f988,f994,f997,f1003])).
% 0.60/0.65 fof(f1024,plain,(
% 0.60/0.65 $false|~sQ14_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f998,f128])).
% 0.60/0.65 fof(f1025,plain,(
% 0.60/0.65 ~sQ14_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1024])).
% 0.60/0.65 fof(f1026,plain,(
% 0.60/0.65 $false|sQ13_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f996,f949])).
% 0.60/0.65 fof(f1027,plain,(
% 0.60/0.65 sQ13_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1026])).
% 0.60/0.65 fof(f1028,plain,(
% 0.60/0.65 $false|sQ12_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f993,f944])).
% 0.60/0.65 fof(f1029,plain,(
% 0.60/0.65 sQ12_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1028])).
% 0.60/0.65 fof(f1030,plain,(
% 0.60/0.65 $false|sQ11_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f990,f941])).
% 0.60/0.65 fof(f1031,plain,(
% 0.60/0.65 sQ11_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1030])).
% 0.60/0.65 fof(f1032,plain,(
% 0.60/0.65 $false|~sQ10_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f986,f132])).
% 0.60/0.65 fof(f1033,plain,(
% 0.60/0.65 ~sQ10_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1032])).
% 0.60/0.65 fof(f1034,plain,(
% 0.60/0.65 $false|~sQ9_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f983,f131])).
% 0.60/0.65 fof(f1035,plain,(
% 0.60/0.65 ~sQ9_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1034])).
% 0.60/0.65 fof(f1036,plain,(
% 0.60/0.65 $false|~sQ8_spl),
% 0.60/0.65 inference(forward_subsumption_resolution,[status(thm)],[f980,f130])).
% 0.60/0.65 fof(f1037,plain,(
% 0.60/0.65 ~sQ8_spl),
% 0.60/0.65 inference(contradiction_clause,[status(thm)],[f1036])).
% 0.60/0.65 fof(f1038,plain,(
% 0.60/0.65 $false),
% 0.60/0.65 inference(sat_refutation,[status(thm)],[f1006,f1020,f1021,f1025,f1027,f1029,f1031,f1033,f1035,f1037])).
% 0.60/0.65 % SZS output end CNFRefutation for theBenchmark.p
% 0.60/0.66 % Elapsed time: 0.283452 seconds
% 0.60/0.66 % CPU time: 1.785810 seconds
% 0.60/0.66 % Total memory used: 136.256 MB
% 0.60/0.66 % Net memory used: 133.983 MB
%------------------------------------------------------------------------------