TSTP Solution File: ALG260^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG260^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : 600s
% DateTime : Thu Jul 14 17:57:48 EDT 2022
% Result : Theorem 0.55s 0.72s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG260^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 02:09:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.72 % SZS status Theorem
% 0.55/0.72 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.55/0.72 % Inferences: 77
% 0.55/0.72 % SZS output start Proof
% 0.55/0.72 thf(def_axvarid,definition,(axvarid = (![X1:term]:(((sub @ X1) @ id) = X1)))).
% 0.55/0.72 thf(def_lamnotvar,definition,(lamnotvar = (![X1:term]:(~((var @ (lam @ X1))))))).
% 0.55/0.72 thf(def_hoaslam,definition,(hoaslam = (^[X1:subst]:(^[X2:subst>term>term]:(lam @ ((X2 @ sh) @ one)))))).
% 0.55/0.72 thf(def_hoasvar,definition,(hoasvar = (^[X1:subst]:(^[X2:term]:(^[X3:subst]:(var @ ((sub @ X2) @ X3))))))).
% 0.55/0.72 thf(def_hoaslamnotvar,definition,(hoaslamnotvar = (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((((hoasvar @ id) @ ((hoaslam @ id) @ X1)) @ id))))))).
% 0.55/0.72 thf(def_hoaslamnotvar_lthm,definition,(hoaslamnotvar_lthm = (axvarid => (lamnotvar => hoaslamnotvar)))).
% 0.55/0.72 thf(thm,conjecture,((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(~((var @ (lam @ X1))))) => (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((var @ ((sub @ (lam @ ((X1 @ sh) @ one))) @ id))))))))).
% 0.55/0.72 thf(h0,negated_conjecture,(~(((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(~((var @ (lam @ X1))))) => (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((var @ ((sub @ (lam @ ((X1 @ sh) @ one))) @ id)))))))))),inference(assume_negation,[status(cth)],[thm])).
% 0.55/0.72 thf(ax1217, axiom, (p1|~(p3)), file('<stdin>', ax1217)).
% 0.55/0.72 thf(ax1219, axiom, ~(p1), file('<stdin>', ax1219)).
% 0.55/0.72 thf(ax1152, axiom, (~(p10)|p71), file('<stdin>', ax1152)).
% 0.55/0.72 thf(ax1204, axiom, (p3|~(p16)), file('<stdin>', ax1204)).
% 0.55/0.72 thf(ax1151, axiom, (~(p71)|p70), file('<stdin>', ax1151)).
% 0.55/0.72 thf(ax1216, axiom, p10, file('<stdin>', ax1216)).
% 0.55/0.72 thf(ax1197, axiom, (p16|~(p23)), file('<stdin>', ax1197)).
% 0.55/0.72 thf(pax2, axiom, (p2=>![X275:term]:(fsub @ X275 @ fid)=(X275)), file('<stdin>', pax2)).
% 0.55/0.72 thf(ax1218, axiom, (p1|p2), file('<stdin>', ax1218)).
% 0.55/0.72 thf(ax1150, axiom, (~(p70)|p23|p69), file('<stdin>', ax1150)).
% 0.55/0.72 thf(pax15, axiom, (p15=>![X211:term]:~(fvar @ (flam @ X211))), file('<stdin>', pax15)).
% 0.55/0.72 thf(ax1205, axiom, (p3|p15), file('<stdin>', ax1205)).
% 0.55/0.72 thf(pax69, axiom, (p69=>![X171:term]:((X171)=(fsub @ (flam @ (f__1 @ fsh @ fone)) @ fid)=>~((![X172:subst, X173:term, X131:subst]:(fsub @ (f__1 @ X172 @ X173) @ X131)=(f__1 @ (fcomp @ X172 @ X131) @ (fsub @ X173 @ X131))=>~(fvar @ X171))))), file('<stdin>', pax69)).
% 0.55/0.72 thf(c_0_13, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1217])).
% 0.55/0.72 thf(c_0_14, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1219])).
% 0.55/0.72 thf(c_0_15, plain, (~p10|p71), inference(fof_simplification,[status(thm)],[ax1152])).
% 0.55/0.72 thf(c_0_16, plain, (p3|~p16), inference(fof_simplification,[status(thm)],[ax1204])).
% 0.55/0.72 thf(c_0_17, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.55/0.72 thf(c_0_18, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_14])).
% 0.55/0.72 thf(c_0_19, plain, (~p71|p70), inference(fof_simplification,[status(thm)],[ax1151])).
% 0.55/0.72 thf(c_0_20, plain, (p71|~p10), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.55/0.72 thf(c_0_21, plain, p10, inference(split_conjunct,[status(thm)],[ax1216])).
% 0.55/0.72 thf(c_0_22, plain, (p16|~p23), inference(fof_simplification,[status(thm)],[ax1197])).
% 0.55/0.72 thf(c_0_23, plain, (p3|~p16), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.55/0.72 thf(c_0_24, plain, ~p3, inference(sr,[status(thm)],[c_0_17, c_0_18])).
% 0.55/0.72 thf(c_0_25, plain, ![X1817:term]:(~p2|(fsub @ X1817 @ fid)=(X1817)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 0.55/0.72 thf(c_0_26, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1218])).
% 0.55/0.72 thf(c_0_27, plain, (~p70|p23|p69), inference(fof_simplification,[status(thm)],[ax1150])).
% 0.55/0.72 thf(c_0_28, plain, (p70|~p71), inference(split_conjunct,[status(thm)],[c_0_19])).
% 0.55/0.72 thf(c_0_29, plain, p71, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 0.55/0.72 thf(c_0_30, plain, (p16|~p23), inference(split_conjunct,[status(thm)],[c_0_22])).
% 0.55/0.72 thf(c_0_31, plain, ~p16, inference(sr,[status(thm)],[c_0_23, c_0_24])).
% 0.55/0.72 thf(c_0_32, plain, ![X1687:term]:(~p15|~fvar @ (flam @ X1687)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax15])])])])).
% 0.55/0.72 thf(c_0_33, plain, (p3|p15), inference(split_conjunct,[status(thm)],[ax1205])).
% 0.55/0.72 thf(c_0_34, plain, ![X1543:term, X1544:subst, X1545:term, X1546:subst]:(((fsub @ (f__1 @ X1544 @ X1545) @ X1546)=(f__1 @ (fcomp @ X1544 @ X1546) @ (fsub @ X1545 @ X1546))|(X1543)!=(fsub @ (flam @ (f__1 @ fsh @ fone)) @ fid)|~p69)&(fvar @ X1543|(X1543)!=(fsub @ (flam @ (f__1 @ fsh @ fone)) @ fid)|~p69)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax69])])])])])).
% 0.55/0.72 thf(c_0_35, plain, ![X1:term]:((fsub @ X1 @ fid)=(X1)|~p2), inference(split_conjunct,[status(thm)],[c_0_25])).
% 0.55/0.72 thf(c_0_36, plain, p2, inference(sr,[status(thm)],[c_0_26, c_0_18])).
% 0.55/0.72 thf(c_0_37, plain, (p23|p69|~p70), inference(split_conjunct,[status(thm)],[c_0_27])).
% 0.55/0.72 thf(c_0_38, plain, p70, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 0.55/0.72 thf(c_0_39, plain, ~p23, inference(sr,[status(thm)],[c_0_30, c_0_31])).
% 0.55/0.72 thf(c_0_40, plain, ![X1:term]:(~p15|~fvar @ (flam @ X1)), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.55/0.72 thf(c_0_41, plain, p15, inference(sr,[status(thm)],[c_0_33, c_0_24])).
% 0.55/0.72 thf(c_0_42, plain, ![X1:term]:(fvar @ X1|(X1)!=(fsub @ (flam @ (f__1 @ fsh @ fone)) @ fid)|~p69), inference(split_conjunct,[status(thm)],[c_0_34])).
% 0.55/0.72 thf(c_0_43, plain, ![X1:term]:(fsub @ X1 @ fid)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 0.55/0.72 thf(c_0_44, plain, p69, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])]), c_0_39])).
% 0.55/0.72 thf(c_0_45, plain, ![X1:term]:~fvar @ (flam @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])).
% 0.55/0.72 thf(c_0_46, plain, ($false), inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43]), c_0_44])])]), c_0_45]), ['proof']).
% 0.55/0.72 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 0.55/0.72 thf(0,theorem,((![X1:term]:(((sub @ X1) @ id) = X1)) => ((![X1:term]:(~((var @ (lam @ X1))))) => (![X1:subst>term>term]:((![X2:subst]:(![X3:term]:(![X4:subst]:(((sub @ ((X1 @ X2) @ X3)) @ X4) = ((X1 @ ((comp @ X2) @ X4)) @ ((sub @ X3) @ X4)))))) => (~((var @ ((sub @ (lam @ ((X1 @ sh) @ one))) @ id)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 0.55/0.72 % SZS output end Proof
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