%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN386^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 03:18:10 PM UTC 2025
% Result : Theorem 23.71s 23.93s
% Output : Proof 23.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN386^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 15:20:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 23.71/23.93 % SZS status Theorem
% 23.71/23.93 % Mode: mode371
% 23.71/23.93 % Inferences: 8
% 23.71/23.93 % SZS output start Proof
% 23.71/23.93 thf(cX2138,conjecture,((~(((~(((![X1:$i]:(~((![X2:$i]:(~(((cF @ X1) @ X2))))))) => (![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(~((![X4:$i]:(((cS @ X3) @ X4) => (((cD @ X4) @ X1) @ X2))))))))))))))) => (~((![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(![X4:$i]:((((cD @ X3) @ X4) @ X2) => (![X5:$i]:(![X6:$i]:((~((((cF @ X3) @ X5) => (~(((cF @ X4) @ X6)))))) => (((cD @ X5) @ X6) @ X1)))))))))))))))))) => (~((![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(~((![X4:$i]:(((cS @ X3) @ X4) => (![X5:$i]:(((cF @ X4) @ X5) => (((cD @ X5) @ X1) @ X2)))))))))))))))))).
% 23.71/23.93 thf(h0,negated_conjecture,(~(((~(((~(((![X1:$i]:(~((![X2:$i]:(~(((cF @ X1) @ X2))))))) => (![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(~((![X4:$i]:(((cS @ X3) @ X4) => (((cD @ X4) @ X1) @ X2))))))))))))))) => (~((![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(![X4:$i]:((((cD @ X3) @ X4) @ X2) => (![X5:$i]:(![X6:$i]:((~((((cF @ X3) @ X5) => (~(((cF @ X4) @ X6)))))) => (((cD @ X5) @ X6) @ X1)))))))))))))))))) => (~((![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(~((![X4:$i]:(((cS @ X3) @ X4) => (![X5:$i]:(((cF @ X4) @ X5) => (((cD @ X5) @ X1) @ X2))))))))))))))))))),inference(assume_negation,[status(cth)],[cX2138])).
% 23.71/23.93 thf(ax7, axiom, (p1|~(p2)), file('<stdin>', ax7)).
% 23.71/23.93 thf(ax8, axiom, ~(p1), file('<stdin>', ax8)).
% 23.71/23.93 thf(nax1, axiom, (p1<=(~((~((![X1:$i]:~(![X2:$i]:~(fcF @ X1 @ X2))=>![X1:$i]:~(![X2:$i]:~(![X3:$i]:~(![X4:$i]:(fcS @ X3 @ X4=>fcD @ X4 @ X1 @ X2))))))=>~(![X1:$i]:~(![X2:$i]:~(![X3:$i, X4:$i]:(fcD @ X3 @ X4 @ X2=>![X5:$i, X6:$i]:(~((fcF @ X3 @ X5=>~(fcF @ X4 @ X6)))=>fcD @ X5 @ X6 @ X1)))))))=>~(![X1:$i]:~(![X2:$i]:~(![X3:$i]:~(![X4:$i]:(fcS @ X3 @ X4=>![X5:$i]:(fcF @ X4 @ X5=>fcD @ X5 @ X1 @ X2)))))))), file('<stdin>', nax1)).
% 23.71/23.93 thf(pax5, axiom, (p5=>![X1:$i]:~(![X2:$i]:~(![X3:$i, X4:$i]:(fcD @ X3 @ X4 @ X2=>![X5:$i, X6:$i]:(~((fcF @ X3 @ X5=>~(fcF @ X4 @ X6)))=>fcD @ X5 @ X6 @ X1))))), file('<stdin>', pax5)).
% 23.71/23.93 thf(ax4, axiom, (p2|p5), file('<stdin>', ax4)).
% 23.71/23.93 thf(c_0_5, plain, (p1|~p2), inference(fof_simplification,[status(thm)],[ax7])).
% 23.71/23.93 thf(c_0_6, plain, ~p1, inference(fof_simplification,[status(thm)],[ax8])).
% 23.71/23.93 thf(c_0_7, plain, (p1|~p2), inference(split_conjunct,[status(thm)],[c_0_5])).
% 23.71/23.93 thf(c_0_8, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_6])).
% 23.71/23.93 thf(c_0_9, plain, ![X114:$i, X117:$i, X119:$i, X120:$i, X122:$i, X123:$i, X124:$i, X125:$i, X126:$i, X128:$i]:((((fcF @ X114 @ (esk56_1 @ X114)|p1)&(~fcS @ (esk58_1 @ X117) @ X119|fcD @ X119 @ esk57_0 @ X117|p1))&(~fcD @ X122 @ X123 @ (esk59_1 @ X120)|(~fcF @ X122 @ X124|~fcF @ X123 @ X125|fcD @ X124 @ X125 @ X120)|p1))&((fcS @ X128 @ (esk61_2 @ X126 @ X128)|p1)&((fcF @ (esk61_2 @ X126 @ X128) @ (esk62_2 @ X126 @ X128)|p1)&(~fcD @ (esk62_2 @ X126 @ X128) @ X126 @ (esk60_1 @ X126)|p1)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])])).
% 23.71/23.93 thf(c_0_10, plain, ![X39:$i, X41:$i, X42:$i, X43:$i, X44:$i]:(~p5|(~fcD @ X41 @ X42 @ (esk17_1 @ X39)|(~fcF @ X41 @ X43|~fcF @ X42 @ X44|fcD @ X43 @ X44 @ X39))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax5])])])])])).
% 23.71/23.93 thf(c_0_11, plain, (p2|p5), inference(split_conjunct,[status(thm)],[ax4])).
% 23.71/23.93 thf(c_0_12, plain, ~p2, inference(sr,[status(thm)],[c_0_7, c_0_8])).
% 23.71/23.93 thf(c_0_13, plain, ![X1:$i, X2:$i]:(fcD @ X2 @ esk57_0 @ X1|p1|~fcS @ (esk58_1 @ X1) @ X2), inference(split_conjunct,[status(thm)],[c_0_9])).
% 23.71/23.93 thf(c_0_14, plain, ![X2:$i, X1:$i]:(fcS @ X1 @ (esk61_2 @ X2 @ X1)|p1), inference(split_conjunct,[status(thm)],[c_0_9])).
% 23.71/23.93 thf(c_0_15, plain, ![X1:$i, X3:$i, X2:$i, X4:$i, X5:$i]:(fcD @ X4 @ X5 @ X3|~p5|~fcD @ X1 @ X2 @ (esk17_1 @ X3)|~fcF @ X1 @ X4|~fcF @ X2 @ X5), inference(split_conjunct,[status(thm)],[c_0_10])).
% 23.71/23.93 thf(c_0_16, plain, p5, inference(sr,[status(thm)],[c_0_11, c_0_12])).
% 23.71/23.93 thf(c_0_17, plain, ![X2:$i, X1:$i]:(fcD @ X1 @ esk57_0 @ X2|~fcS @ (esk58_1 @ X2) @ X1), inference(sr,[status(thm)],[c_0_13, c_0_8])).
% 23.71/23.93 thf(c_0_18, plain, ![X2:$i, X1:$i]:fcS @ X1 @ (esk61_2 @ X2 @ X1), inference(sr,[status(thm)],[c_0_14, c_0_8])).
% 23.71/23.93 thf(c_0_19, plain, ![X3:$i, X5:$i, X4:$i, X2:$i, X1:$i]:(fcD @ X1 @ X2 @ X3|~fcD @ X4 @ X5 @ (esk17_1 @ X3)|~fcF @ X5 @ X2|~fcF @ X4 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])).
% 23.71/23.93 thf(c_0_20, plain, ![X1:$i, X2:$i]:fcD @ (esk61_2 @ X1 @ (esk58_1 @ X2)) @ esk57_0 @ X2, inference(spm,[status(thm)],[c_0_17, c_0_18])).
% 23.71/23.93 thf(c_0_21, plain, ![X1:$i, X2:$i]:(fcF @ (esk61_2 @ X1 @ X2) @ (esk62_2 @ X1 @ X2)|p1), inference(split_conjunct,[status(thm)],[c_0_9])).
% 23.71/23.93 thf(c_0_22, plain, ![X2:$i, X1:$i]:(p1|~fcD @ (esk62_2 @ X1 @ X2) @ X1 @ (esk60_1 @ X1)), inference(split_conjunct,[status(thm)],[c_0_9])).
% 23.71/23.93 thf(c_0_23, plain, ![X1:$i, X4:$i, X3:$i, X2:$i]:(fcD @ X1 @ X2 @ X3|~fcF @ (esk61_2 @ X4 @ (esk58_1 @ (esk17_1 @ X3))) @ X1|~fcF @ esk57_0 @ X2), inference(spm,[status(thm)],[c_0_19, c_0_20])).
% 23.71/23.93 thf(c_0_24, plain, ![X1:$i, X2:$i]:fcF @ (esk61_2 @ X1 @ X2) @ (esk62_2 @ X1 @ X2), inference(sr,[status(thm)],[c_0_21, c_0_8])).
% 23.71/23.93 thf(c_0_25, plain, ![X2:$i, X1:$i]:~fcD @ (esk62_2 @ X1 @ X2) @ X1 @ (esk60_1 @ X1), inference(sr,[status(thm)],[c_0_22, c_0_8])).
% 23.71/23.93 thf(c_0_26, plain, ![X1:$i, X2:$i, X3:$i]:(fcD @ (esk62_2 @ X1 @ (esk58_1 @ (esk17_1 @ X2))) @ X3 @ X2|~fcF @ esk57_0 @ X3), inference(spm,[status(thm)],[c_0_23, c_0_24])).
% 23.71/23.93 thf(c_0_27, plain, ![X1:$i]:(fcF @ X1 @ (esk56_1 @ X1)|p1), inference(split_conjunct,[status(thm)],[c_0_9])).
% 23.71/23.93 thf(c_0_28, plain, ![X1:$i]:~fcF @ esk57_0 @ X1, inference(spm,[status(thm)],[c_0_25, c_0_26])).
% 23.71/23.93 thf(c_0_29, plain, ![X1:$i]:fcF @ X1 @ (esk56_1 @ X1), inference(sr,[status(thm)],[c_0_27, c_0_8])).
% 23.71/23.93 thf(c_0_30, plain, ($false), inference(spm,[status(thm)],[c_0_28, c_0_29]), ['proof']).
% 23.71/23.93 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 23.71/23.93 thf(0,theorem,((~(((~(((![X1:$i]:(~((![X2:$i]:(~(((cF @ X1) @ X2))))))) => (![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(~((![X4:$i]:(((cS @ X3) @ X4) => (((cD @ X4) @ X1) @ X2))))))))))))))) => (~((![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(![X4:$i]:((((cD @ X3) @ X4) @ X2) => (![X5:$i]:(![X6:$i]:((~((((cF @ X3) @ X5) => (~(((cF @ X4) @ X6)))))) => (((cD @ X5) @ X6) @ X1)))))))))))))))))) => (~((![X1:$i]:(~((![X2:$i]:(~((![X3:$i]:(~((![X4:$i]:(((cS @ X3) @ X4) => (![X5:$i]:(((cF @ X4) @ X5) => (((cD @ X5) @ X1) @ X2))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 23.71/23.93 % SZS output end Proof
%------------------------------------------------------------------------------