%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL955^24 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 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 : Mon Sep 7 01:02:57 PM UTC 2026 % Result : Theorem 65.98s 66.44s % Output : Proof 65.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL955^24 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.08/0.36 % Computer : n006.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Sat Sep 5 09:13:46 UTC 2026 % 0.14/0.36 % CPUTime : % 65.98/66.44 % SZS status Theorem % 65.98/66.44 % Mode: mode8a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 65.98/66.44 % Inferences: 3326 % 65.98/66.44 % SZS output start Proof % 65.98/66.44 thf(ty_mworld, type, mworld : $tType). % 65.98/66.44 thf(ty_eigen__14, type, eigen__14 : mworld). % 65.98/66.44 thf(ty_eigen__2, type, eigen__2 : mworld). % 65.98/66.44 thf(ty_eigen__15, type, eigen__15 : mworld). % 65.98/66.44 thf(ty_eigen__1, type, eigen__1 : mworld). % 65.98/66.44 thf(ty_eigen__0, type, eigen__0 : mworld). % 65.98/66.44 thf(ty_pv65, type, pv65 : $i). % 65.98/66.44 thf(ty_gt, type, gt : ($i>$i>mworld>$o)). % 65.98/66.44 thf(ty_mrel, type, mrel : (mworld>mworld>$o)). % 65.98/66.44 thf(ty_plus, type, plus : ($i>$i>$i)). % 65.98/66.44 thf(ty_n1, type, n1 : $i). % 65.98/66.44 thf(ty_tptp_float_0_001, type, tptp_float_0_001 : $i). % 65.98/66.44 thf(ty_mactual, type, mactual : mworld). % 65.98/66.44 thf(ty_loopcounter, type, loopcounter : $i). % 65.98/66.44 thf(ty_geq, type, geq : ($i>$i>mworld>$o)). % 65.98/66.44 thf(ty_true, type, true : (mworld>$o)). % 65.98/66.44 thf(sP1,plain,sP1 <=> ((mrel @ mactual) @ eigen__15),introduced(definition,[new_symbols(definition,[sP1])])). % 65.98/66.44 thf(sP2,plain,sP2 <=> (true @ eigen__15),introduced(definition,[new_symbols(definition,[sP2])])). % 65.98/66.44 thf(sP3,plain,sP3 <=> ((mrel @ mactual) @ eigen__2),introduced(definition,[new_symbols(definition,[sP3])])). % 65.98/66.44 thf(sP4,plain,sP4 <=> (sP1 => sP2),introduced(definition,[new_symbols(definition,[sP4])])). % 65.98/66.44 thf(sP5,plain,sP5 <=> ((!!) @ (mrel @ mactual)),introduced(definition,[new_symbols(definition,[sP5])])). % 65.98/66.44 thf(sP6,plain,sP6 <=> (true @ eigen__2),introduced(definition,[new_symbols(definition,[sP6])])). % 65.98/66.44 thf(sP7,plain,sP7 <=> (![X1:mworld]:((!!) @ (mrel @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 65.98/66.44 thf(sP8,plain,sP8 <=> (sP3 => sP6),introduced(definition,[new_symbols(definition,[sP8])])). % 65.98/66.44 thf(sP9,plain,sP9 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (true @ X1))),introduced(definition,[new_symbols(definition,[sP9])])). % 65.98/66.44 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 65.98/66.44 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 65.98/66.44 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 65.98/66.44 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 65.98/66.44 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 65.98/66.44 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 65.98/66.44 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 65.98/66.44 thf(cl5_nebula_array_0028,conjecture,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((geq @ pv65) @ tptp_float_0_001) @ X2))) => (~(((![X2:mworld]:(((mrel @ X1) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X4))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (true @ X3)))))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (true @ X3))))))))))))))). % 65.98/66.44 thf(h0,negated_conjecture,(~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((geq @ pv65) @ tptp_float_0_001) @ X2))) => (~(((![X2:mworld]:(((mrel @ X1) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X4))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (true @ X3)))))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (true @ X3)))))))))))))))),inference(assume_negation,[status(cth)],[cl5_nebula_array_0028])). % 65.98/66.44 thf(h1,assumption,(~((((mrel @ mactual) @ eigen__0) => ((![X1:mworld]:(((mrel @ eigen__0) @ X1) => (((geq @ pv65) @ tptp_float_0_001) @ X1))) => (~(((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))) => (~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2))))))))))))))),introduced(assumption,[])). % 65.98/66.44 thf(h2,assumption,((mrel @ mactual) @ eigen__0),introduced(assumption,[])). % 65.98/66.44 thf(h3,assumption,(~(((![X1:mworld]:(((mrel @ eigen__0) @ X1) => (((geq @ pv65) @ tptp_float_0_001) @ X1))) => (~(((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))) => (~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))))))))))),introduced(assumption,[])). % 65.98/66.44 thf(h4,assumption,(![X1:mworld]:(((mrel @ eigen__0) @ X1) => (((geq @ pv65) @ tptp_float_0_001) @ X1))),introduced(assumption,[])). % 65.98/66.44 thf(h5,assumption,((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))) => (~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2))))))))),introduced(assumption,[])). % 65.98/66.44 thf(h6,assumption,(~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))))),introduced(assumption,[])). % 65.98/66.44 thf(h7,assumption,(~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))))),introduced(assumption,[])). % 65.98/66.44 thf(h8,assumption,(~((((mrel @ eigen__0) @ eigen__1) => ((![X1:mworld]:(((mrel @ eigen__1) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))))))) => (![X1:mworld]:(((mrel @ eigen__1) @ X1) => (true @ X1))))))),introduced(assumption,[])). % 65.98/66.44 thf(h9,assumption,((mrel @ eigen__0) @ eigen__1),introduced(assumption,[])). % 65.98/66.44 thf(h10,assumption,(~(((![X1:mworld]:(((mrel @ eigen__1) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))))))) => (![X1:mworld]:(((mrel @ eigen__1) @ X1) => (true @ X1)))))),introduced(assumption,[])). % 65.98/66.44 thf(h11,assumption,(![X1:mworld]:(((mrel @ eigen__1) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X2))))))),introduced(assumption,[])). % 65.98/66.44 thf(h12,assumption,(~((![X1:mworld]:(((mrel @ eigen__1) @ X1) => (true @ X1))))),introduced(assumption,[])). % 65.98/66.44 thf(h13,assumption,(~((((mrel @ eigen__1) @ eigen__2) => sP6))),introduced(assumption,[])). % 65.98/66.44 thf(h14,assumption,((mrel @ eigen__1) @ eigen__2),introduced(assumption,[])). % 65.98/66.44 thf(h15,assumption,(~(sP6)),introduced(assumption,[])). % 65.98/66.44 thf(1,plain,(~(sP5) | sP3),inference(all_rule,[status(thm)],[])). % 65.98/66.44 thf(2,plain,((~(sP8) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])). % 65.98/66.44 thf(3,plain,(~(sP9) | sP8),inference(all_rule,[status(thm)],[])). % 65.98/66.44 thf(4,plain,(~(sP7) | sP5),inference(all_rule,[status(thm)],[])). % 65.98/66.44 thf(ttrue,axiom,(mlocal @ (mbox @ true))). % 65.98/66.44 thf(5,plain,sP9,inference(preprocess,[status(thm)],[ttrue]). % 65.98/66.44 thf(mrel_universal,axiom,sP7). % 65.98/66.44 thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h10,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,h15,5,mrel_universal])). % 65.98/66.44 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,6,h14,h15])). % 65.98/66.44 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,7,h13])). % 65.98/66.44 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,8,h11,h12])). % 65.98/66.44 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,9,h9,h10])). % 65.98/66.44 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,10,h8])). % 65.98/66.44 thf(h16,assumption,(~((((mrel @ eigen__0) @ eigen__14) => ((![X1:mworld]:(((mrel @ eigen__14) @ X1) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X1))) => (![X1:mworld]:(((mrel @ eigen__14) @ X1) => (true @ X1))))))),introduced(assumption,[])). % 65.98/66.44 thf(h17,assumption,((mrel @ eigen__0) @ eigen__14),introduced(assumption,[])). % 65.98/66.44 thf(h18,assumption,(~(((![X1:mworld]:(((mrel @ eigen__14) @ X1) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X1))) => (![X1:mworld]:(((mrel @ eigen__14) @ X1) => (true @ X1)))))),introduced(assumption,[])). % 65.98/66.44 thf(h19,assumption,(![X1:mworld]:(((mrel @ eigen__14) @ X1) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X1))),introduced(assumption,[])). % 65.98/66.44 thf(h20,assumption,(~((![X1:mworld]:(((mrel @ eigen__14) @ X1) => (true @ X1))))),introduced(assumption,[])). % 65.98/66.44 thf(h21,assumption,(~((((mrel @ eigen__14) @ eigen__15) => sP2))),introduced(assumption,[])). % 65.98/66.44 thf(h22,assumption,((mrel @ eigen__14) @ eigen__15),introduced(assumption,[])). % 65.98/66.44 thf(h23,assumption,(~(sP2)),introduced(assumption,[])). % 65.98/66.44 thf(12,plain,(~(sP5) | sP1),inference(all_rule,[status(thm)],[])). % 65.98/66.44 thf(13,plain,((~(sP4) | ~(sP1)) | sP2),inference(prop_rule,[status(thm)],[])). % 65.98/66.44 thf(14,plain,(~(sP9) | sP4),inference(all_rule,[status(thm)],[])). % 65.98/66.44 thf(15,plain,(~(sP7) | sP5),inference(all_rule,[status(thm)],[])). % 65.98/66.44 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h19,h20,h17,h18,h16,h7,h4,h5,h2,h3,h1,h0])],[12,13,14,15,h23,5,mrel_universal])). % 65.98/66.44 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h17,h18,h16,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,16,h22,h23])). % 65.98/66.44 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h16,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__15)],[h20,17,h21])). % 65.98/66.44 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,18,h19,h20])). % 65.98/66.44 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,19,h17,h18])). % 65.98/66.44 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__14)],[h7,20,h16])). % 65.98/66.44 thf(22,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,11,21,h6,h7])). % 65.98/66.44 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,22,h4,h5])). % 65.98/66.44 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,23,h2,h3])). % 65.98/66.44 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,24,h1])). % 65.98/66.44 thf(0,theorem,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((geq @ pv65) @ tptp_float_0_001) @ X2))) => (~(((![X2:mworld]:(((mrel @ X1) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X4))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (true @ X3)))))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((gt @ ((plus @ n1) @ loopcounter)) @ n1) @ X3))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (true @ X3)))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[25,h0])). % 65.98/66.44 % SZS output end Proof %------------------------------------------------------------------------------