%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU999^5 : 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 : n017.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 02:53:04 PM UTC 2025
% Result : Theorem 25.73s 25.86s
% Output : Proof 25.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU999^5 : TPTP v9.2.0. Released v4.0.0.
% 0.09/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 8 20:40:23 EDT 2025
% 0.15/0.36 % CPUTime :
% 25.73/25.86 % SZS status Theorem
% 25.73/25.86 % Mode: mode371
% 25.73/25.86 % Inferences: 25
% 25.73/25.86 % SZS output start Proof
% 25.73/25.86 thf(cPENTAGON_THM2B_pme,conjecture,(![X1:a>a>a]:(![X2:a>a>a]:((~(((~(((~(((~(((~(((~(((~(((![X3:a]:(((X1 @ X3) @ X3) = X3)) => (~((![X3:a]:(((X2 @ X3) @ X3) = X3))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X1 @ ((X1 @ X3) @ X4)) @ X5) = ((X1 @ X3) @ ((X1 @ X4) @ X5))))))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X2 @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ X3) @ ((X2 @ X4) @ X5))))))))))) => (~((![X3:a]:(![X4:a]:(((X1 @ X3) @ X4) = ((X1 @ X4) @ X3))))))))) => (~((![X3:a]:(![X4:a]:(((X2 @ X3) @ X4) = ((X2 @ X4) @ X3))))))))) => (~((![X3:a]:(![X4:a]:(((X1 @ ((X2 @ X3) @ X4)) @ X4) = X4)))))))) => (~((![X3:a]:(![X4:a]:(((X2 @ ((X1 @ X3) @ X4)) @ X4) = X4)))))))) => ((~((![X3:a]:(![X4:a]:(![X5:a]:(![X6:a]:(![X7:a]:((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~((X5 = X6))) => (X5 = X7)))) => (X5 = X3)))) => (X5 = X4)))) => (X6 = X7)))) => (X6 = X3)))) => (X6 = X4)))) => (X7 = X3)))) => (X7 = X4)))) => (X3 = X4)))) => (~((((X2 @ X3) @ X4) = X4)))))) => (~((((X1 @ X3) @ X4) = X3)))))) => (~((((X2 @ X3) @ X5) = X5)))))) => (~((((X1 @ X3) @ X5) = X3)))))) => (~((((X2 @ X3) @ X6) = X6)))))) => (~((((X1 @ X3) @ X6) = X3)))))) => (~((((X2 @ X3) @ X7) = X7)))))) => (~((((X1 @ X3) @ X7) = X3)))))) => (~((((X2 @ X5) @ X6) = X4)))))) => (~((((X1 @ X5) @ X6) = X3)))))) => (~((((X2 @ X5) @ X7) = X5)))))) => (~((((X1 @ X5) @ X7) = X7)))))) => (~((((X2 @ X5) @ X4) = X4)))))) => (~((((X1 @ X5) @ X4) = X5)))))) => (~((((X2 @ X6) @ X7) = X4)))))) => (~((((X1 @ X6) @ X7) = X3)))))) => (~((((X2 @ X6) @ X4) = X4)))))) => (~((((X1 @ X6) @ X4) = X6)))))) => (~((((X2 @ X7) @ X4) = X4)))))) => (~((((X1 @ X7) @ X4) = X7))))))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X1 @ X3) @ ((X2 @ X4) @ ((X1 @ X3) @ X5))) = ((X2 @ ((X1 @ X3) @ X4)) @ ((X1 @ X3) @ X5))))))))))))).
% 25.73/25.86 thf(h0,negated_conjecture,(~((![X1:a>a>a]:(![X2:a>a>a]:((~(((~(((~(((~(((~(((~(((~(((![X3:a]:(((X1 @ X3) @ X3) = X3)) => (~((![X3:a]:(((X2 @ X3) @ X3) = X3))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X1 @ ((X1 @ X3) @ X4)) @ X5) = ((X1 @ X3) @ ((X1 @ X4) @ X5))))))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X2 @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ X3) @ ((X2 @ X4) @ X5))))))))))) => (~((![X3:a]:(![X4:a]:(((X1 @ X3) @ X4) = ((X1 @ X4) @ X3))))))))) => (~((![X3:a]:(![X4:a]:(((X2 @ X3) @ X4) = ((X2 @ X4) @ X3))))))))) => (~((![X3:a]:(![X4:a]:(((X1 @ ((X2 @ X3) @ X4)) @ X4) = X4)))))))) => (~((![X3:a]:(![X4:a]:(((X2 @ ((X1 @ X3) @ X4)) @ X4) = X4)))))))) => ((~((![X3:a]:(![X4:a]:(![X5:a]:(![X6:a]:(![X7:a]:((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~((X5 = X6))) => (X5 = X7)))) => (X5 = X3)))) => (X5 = X4)))) => (X6 = X7)))) => (X6 = X3)))) => (X6 = X4)))) => (X7 = X3)))) => (X7 = X4)))) => (X3 = X4)))) => (~((((X2 @ X3) @ X4) = X4)))))) => (~((((X1 @ X3) @ X4) = X3)))))) => (~((((X2 @ X3) @ X5) = X5)))))) => (~((((X1 @ X3) @ X5) = X3)))))) => (~((((X2 @ X3) @ X6) = X6)))))) => (~((((X1 @ X3) @ X6) = X3)))))) => (~((((X2 @ X3) @ X7) = X7)))))) => (~((((X1 @ X3) @ X7) = X3)))))) => (~((((X2 @ X5) @ X6) = X4)))))) => (~((((X1 @ X5) @ X6) = X3)))))) => (~((((X2 @ X5) @ X7) = X5)))))) => (~((((X1 @ X5) @ X7) = X7)))))) => (~((((X2 @ X5) @ X4) = X4)))))) => (~((((X1 @ X5) @ X4) = X5)))))) => (~((((X2 @ X6) @ X7) = X4)))))) => (~((((X1 @ X6) @ X7) = X3)))))) => (~((((X2 @ X6) @ X4) = X4)))))) => (~((((X1 @ X6) @ X4) = X6)))))) => (~((((X2 @ X7) @ X4) = X4)))))) => (~((((X1 @ X7) @ X4) = X7))))))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X1 @ X3) @ ((X2 @ X4) @ ((X1 @ X3) @ X5))) = ((X2 @ ((X1 @ X3) @ X4)) @ ((X1 @ X3) @ X5)))))))))))))),inference(assume_negation,[status(cth)],[cPENTAGON_THM2B_pme])).
% 25.73/25.86 thf(ax53, axiom, (p1|~(p2)), file('<stdin>', ax53)).
% 25.73/25.86 thf(ax54, axiom, ~(p1), file('<stdin>', ax54)).
% 25.73/25.86 thf(ax52, axiom, (p2|~(p3)), file('<stdin>', ax52)).
% 25.73/25.86 thf(ax50, axiom, (p3|~(p5)), file('<stdin>', ax50)).
% 25.73/25.86 thf(nax2, axiom, (p2<=![X6:a > a > a]:(~((~((~((~((~((~((~((![X2:a]:(f__0 @ X2 @ X2)=(X2)=>~(![X2:a]:(X6 @ X2 @ X2)=(X2))))=>~(![X2:a, X3:a, X4:a]:(f__0 @ (f__0 @ X2 @ X3) @ X4)=(f__0 @ X2 @ (f__0 @ X3 @ X4)))))=>~(![X2:a, X3:a, X4:a]:(X6 @ (X6 @ X2 @ X3) @ X4)=(X6 @ X2 @ (X6 @ X3 @ X4)))))=>~(![X2:a, X3:a]:(f__0 @ X2 @ X3)=(f__0 @ X3 @ X2))))=>~(![X2:a, X3:a]:(X6 @ X2 @ X3)=(X6 @ X3 @ X2))))=>~(![X2:a, X3:a]:(f__0 @ (X6 @ X2 @ X3) @ X3)=(X3))))=>~(![X2:a, X3:a]:(X6 @ (f__0 @ X2 @ X3) @ X3)=(X3))))=>(~(![X2:a, X3:a, X4:a, X5:a, X7:a]:(~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((X4)=(X5))=>(X4)=(X7)))=>(X4)=(X2)))=>(X4)=(X3)))=>(X5)=(X7)))=>(X5)=(X2)))=>(X5)=(X3)))=>(X7)=(X2)))=>(X7)=(X3)))=>(X2)=(X3)))=>~((X6 @ X2 @ X3)=(X3))))=>~((f__0 @ X2 @ X3)=(X2))))=>~((X6 @ X2 @ X4)=(X4))))=>~((f__0 @ X2 @ X4)=(X2))))=>~((X6 @ X2 @ X5)=(X5))))=>~((f__0 @ X2 @ X5)=(X2))))=>~((X6 @ X2 @ X7)=(X7))))=>~((f__0 @ X2 @ X7)=(X2))))=>~((X6 @ X4 @ X5)=(X3))))=>~((f__0 @ X4 @ X5)=(X2))))=>~((X6 @ X4 @ X7)=(X4))))=>~((f__0 @ X4 @ X7)=(X7))))=>~((X6 @ X4 @ X3)=(X3))))=>~((f__0 @ X4 @ X3)=(X4))))=>~((X6 @ X5 @ X7)=(X3))))=>~((f__0 @ X5 @ X7)=(X2))))=>~((X6 @ X5 @ X3)=(X3))))=>~((f__0 @ X5 @ X3)=(X5))))=>~((X6 @ X7 @ X3)=(X3))))=>~((f__0 @ X7 @ X3)=(X7))))=>~(![X2:a, X3:a, X4:a]:(f__0 @ X2 @ (X6 @ X3 @ (f__0 @ X2 @ X4)))=(X6 @ (f__0 @ X2 @ X3) @ (f__0 @ X2 @ X4)))))), file('<stdin>', nax2)).
% 25.73/25.86 thf(ax14, axiom, (~(p28)|p45), file('<stdin>', ax14)).
% 25.73/25.86 thf(ax47, axiom, (p5|~(p8)), file('<stdin>', ax47)).
% 25.73/25.86 thf(pax42, axiom, (p42=>((f__0 @ f__2 @ f__4)=(f__0 @ f__4 @ f__2)=>~(![X1:a, X2:a, X3:a]:(~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((X1)=(X2))=>(X1)=(X3)))=>(X1)=(f__2)))=>(X1)=(f__4)))=>(X2)=(X3)))=>(X2)=(f__2)))=>(X2)=(f__4)))=>(X3)=(f__2)))=>(X3)=(f__4)))=>(f__2)=(f__4)))=>~((f__1 @ f__2 @ f__4)=(f__4))))=>~((f__0 @ f__4 @ f__2)=(f__2))))=>~((f__1 @ f__2 @ X1)=(X1))))=>~((f__0 @ f__2 @ X1)=(f__2))))=>~((f__1 @ f__2 @ X2)=(X2))))=>~((f__0 @ f__2 @ X2)=(f__2))))=>~((f__1 @ f__2 @ X3)=(X3))))=>~((f__0 @ f__2 @ X3)=(f__2))))=>~((f__1 @ X1 @ X2)=(f__4))))=>~((f__0 @ X1 @ X2)=(f__2))))=>~((f__1 @ X1 @ X3)=(X1))))=>~((f__0 @ X1 @ X3)=(X3))))=>~((f__1 @ X1 @ f__4)=(f__4))))=>~((f__0 @ X1 @ f__4)=(X1))))=>~((f__1 @ X2 @ X3)=(f__4))))=>~((f__0 @ X2 @ X3)=(f__2))))=>~((f__1 @ X2 @ f__4)=(f__4))))=>~((f__0 @ X2 @ f__4)=(X2))))=>~((f__1 @ X3 @ f__4)=(f__4))))=>~((f__0 @ X3 @ f__4)=(X3)))))), file('<stdin>', pax42)).
% 25.73/25.86 thf(ax13, axiom, (~(p45)|p44), file('<stdin>', ax13)).
% 25.73/25.86 thf(ax33, axiom, p28, file('<stdin>', ax33)).
% 25.73/25.86 thf(ax43, axiom, (p8|~(p12)), file('<stdin>', ax43)).
% 25.73/25.86 thf(ax12, axiom, (~(p44)|p18|p43), file('<stdin>', ax12)).
% 25.73/25.86 thf(ax37, axiom, (p12|~(p18)), file('<stdin>', ax37)).
% 25.73/25.86 thf(nax3, axiom, (p3<=(~((~((~((~((~((~((~((![X1:a]:(f__0 @ X1 @ X1)=(X1)=>~(![X1:a]:(f__1 @ X1 @ X1)=(X1))))=>~(![X1:a, X2:a, X3:a]:(f__0 @ (f__0 @ X1 @ X2) @ X3)=(f__0 @ X1 @ (f__0 @ X2 @ X3)))))=>~(![X1:a, X2:a, X3:a]:(f__1 @ (f__1 @ X1 @ X2) @ X3)=(f__1 @ X1 @ (f__1 @ X2 @ X3)))))=>~(![X1:a, X2:a]:(f__0 @ X1 @ X2)=(f__0 @ X2 @ X1))))=>~(![X1:a, X2:a]:(f__1 @ X1 @ X2)=(f__1 @ X2 @ X1))))=>~(![X1:a, X2:a]:(f__0 @ (f__1 @ X1 @ X2) @ X2)=(X2))))=>~(![X1:a, X2:a]:(f__1 @ (f__0 @ X1 @ X2) @ X2)=(X2))))=>(~(![X1:a, X2:a, X3:a, X4:a, X5:a]:(~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((X3)=(X4))=>(X3)=(X5)))=>(X3)=(X1)))=>(X3)=(X2)))=>(X4)=(X5)))=>(X4)=(X1)))=>(X4)=(X2)))=>(X5)=(X1)))=>(X5)=(X2)))=>(X1)=(X2)))=>~((f__1 @ X1 @ X2)=(X2))))=>~((f__0 @ X1 @ X2)=(X1))))=>~((f__1 @ X1 @ X3)=(X3))))=>~((f__0 @ X1 @ X3)=(X1))))=>~((f__1 @ X1 @ X4)=(X4))))=>~((f__0 @ X1 @ X4)=(X1))))=>~((f__1 @ X1 @ X5)=(X5))))=>~((f__0 @ X1 @ X5)=(X1))))=>~((f__1 @ X3 @ X4)=(X2))))=>~((f__0 @ X3 @ X4)=(X1))))=>~((f__1 @ X3 @ X5)=(X3))))=>~((f__0 @ X3 @ X5)=(X5))))=>~((f__1 @ X3 @ X2)=(X2))))=>~((f__0 @ X3 @ X2)=(X3))))=>~((f__1 @ X4 @ X5)=(X2))))=>~((f__0 @ X4 @ X5)=(X1))))=>~((f__1 @ X4 @ X2)=(X2))))=>~((f__0 @ X4 @ X2)=(X4))))=>~((f__1 @ X5 @ X2)=(X2))))=>~((f__0 @ X5 @ X2)=(X5))))=>~(![X1:a, X2:a, X3:a]:(f__0 @ X1 @ (f__1 @ X2 @ (f__0 @ X1 @ X3)))=(f__1 @ (f__0 @ X1 @ X2) @ (f__0 @ X1 @ X3)))))), file('<stdin>', nax3)).
% 25.73/25.86 thf(ax11, axiom, (~(p43)|p42), file('<stdin>', ax11)).
% 25.73/25.86 thf(c_0_15, plain, (p1|~p2), inference(fof_simplification,[status(thm)],[ax53])).
% 25.73/25.86 thf(c_0_16, plain, ~p1, inference(fof_simplification,[status(thm)],[ax54])).
% 25.73/25.86 thf(c_0_17, plain, (p2|~p3), inference(fof_simplification,[status(thm)],[ax52])).
% 25.73/25.86 thf(c_0_18, plain, (p1|~p2), inference(split_conjunct,[status(thm)],[c_0_15])).
% 25.73/25.86 thf(c_0_19, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_16])).
% 25.73/25.86 thf(c_0_20, plain, ![X6:a > a > a]:(epred12_1 @ X6<=>(~(![X2:a, X3:a, X4:a, X5:a, X7:a]:(~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((X4)=(X5))=>(X4)=(X7)))=>(X4)=(X2)))=>(X4)=(X3)))=>(X5)=(X7)))=>(X5)=(X2)))=>(X5)=(X3)))=>(X7)=(X2)))=>(X7)=(X3)))=>(X2)=(X3)))=>~((X6 @ X2 @ X3)=(X3))))=>~((f__0 @ X2 @ X3)=(X2))))=>~((X6 @ X2 @ X4)=(X4))))=>~((f__0 @ X2 @ X4)=(X2))))=>~((X6 @ X2 @ X5)=(X5))))=>~((f__0 @ X2 @ X5)=(X2))))=>~((X6 @ X2 @ X7)=(X7))))=>~((f__0 @ X2 @ X7)=(X2))))=>~((X6 @ X4 @ X5)=(X3))))=>~((f__0 @ X4 @ X5)=(X2))))=>~((X6 @ X4 @ X7)=(X4))))=>~((f__0 @ X4 @ X7)=(X7))))=>~((X6 @ X4 @ X3)=(X3))))=>~((f__0 @ X4 @ X3)=(X4))))=>~((X6 @ X5 @ X7)=(X3))))=>~((f__0 @ X5 @ X7)=(X2))))=>~((X6 @ X5 @ X3)=(X3))))=>~((f__0 @ X5 @ X3)=(X5))))=>~((X6 @ X7 @ X3)=(X3))))=>~((f__0 @ X7 @ X3)=(X7))))=>~(![X2:a, X3:a, X4:a]:(f__0 @ X2 @ (X6 @ X3 @ (f__0 @ X2 @ X4)))=(X6 @ (f__0 @ X2 @ X3) @ (f__0 @ X2 @ X4))))), introduced(definition)).
% 25.73/25.86 thf(c_0_21, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax50])).
% 25.73/25.86 thf(c_0_22, plain, (p2|~p3), inference(split_conjunct,[status(thm)],[c_0_17])).
% 25.73/25.86 thf(c_0_23, plain, ~p2, inference(sr,[status(thm)],[c_0_18, c_0_19])).
% 25.73/25.86 thf(c_0_24, plain, (epred4_0<=>![X1:a, X2:a, X3:a]:(~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((X1)=(X2))=>(X1)=(X3)))=>(X1)=(f__2)))=>(X1)=(f__4)))=>(X2)=(X3)))=>(X2)=(f__2)))=>(X2)=(f__4)))=>(X3)=(f__2)))=>(X3)=(f__4)))=>(f__2)=(f__4)))=>~((f__1 @ f__2 @ f__4)=(f__4))))=>~((f__0 @ f__4 @ f__2)=(f__2))))=>~((f__1 @ f__2 @ X1)=(X1))))=>~((f__0 @ f__2 @ X1)=(f__2))))=>~((f__1 @ f__2 @ X2)=(X2))))=>~((f__0 @ f__2 @ X2)=(f__2))))=>~((f__1 @ f__2 @ X3)=(X3))))=>~((f__0 @ f__2 @ X3)=(f__2))))=>~((f__1 @ X1 @ X2)=(f__4))))=>~((f__0 @ X1 @ X2)=(f__2))))=>~((f__1 @ X1 @ X3)=(X1))))=>~((f__0 @ X1 @ X3)=(X3))))=>~((f__1 @ X1 @ f__4)=(f__4))))=>~((f__0 @ X1 @ f__4)=(X1))))=>~((f__1 @ X2 @ X3)=(f__4))))=>~((f__0 @ X2 @ X3)=(f__2))))=>~((f__1 @ X2 @ f__4)=(f__4))))=>~((f__0 @ X2 @ f__4)=(X2))))=>~((f__1 @ X3 @ f__4)=(f__4))))=>~((f__0 @ X3 @ f__4)=(X3)))), introduced(definition)).
% 25.73/25.86 thf(c_0_25, axiom, (p2<=![X6:a > a > a]:(~((~((~((~((~((~((~((![X2:a]:(f__0 @ X2 @ X2)=(X2)=>~(![X2:a]:(X6 @ X2 @ X2)=(X2))))=>~(![X2:a, X3:a, X4:a]:(f__0 @ (f__0 @ X2 @ X3) @ X4)=(f__0 @ X2 @ (f__0 @ X3 @ X4)))))=>~(![X2:a, X3:a, X4:a]:(X6 @ (X6 @ X2 @ X3) @ X4)=(X6 @ X2 @ (X6 @ X3 @ X4)))))=>~(![X2:a, X3:a]:(f__0 @ X2 @ X3)=(f__0 @ X3 @ X2))))=>~(![X2:a, X3:a]:(X6 @ X2 @ X3)=(X6 @ X3 @ X2))))=>~(![X2:a, X3:a]:(f__0 @ (X6 @ X2 @ X3) @ X3)=(X3))))=>~(![X2:a, X3:a]:(X6 @ (f__0 @ X2 @ X3) @ X3)=(X3))))=>epred12_1 @ X6)), inference(apply_def,[status(thm)],[nax2, c_0_20])).
% 25.73/25.86 thf(c_0_26, plain, (~p28|p45), inference(fof_simplification,[status(thm)],[ax14])).
% 25.73/25.86 thf(c_0_27, plain, (p5|~p8), inference(fof_simplification,[status(thm)],[ax47])).
% 25.73/25.86 thf(c_0_28, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_21])).
% 25.73/25.86 thf(c_0_29, plain, ~p3, inference(sr,[status(thm)],[c_0_22, c_0_23])).
% 25.73/25.86 thf(c_0_30, axiom, (p42=>((f__0 @ f__2 @ f__4)=(f__0 @ f__4 @ f__2)=>~(epred4_0))), inference(apply_def,[status(thm)],[pax42, c_0_24])).
% 25.73/25.86 thf(c_0_31, plain, ![X290:a, X291:a, X292:a, X293:a, X294:a, X295:a, X296:a, X297:a, X298:a, X299:a, X300:a, X301:a, X302:a, X303:a, X304:a, X305:a]:((((((((((f__0 @ X290 @ X290)=(X290)|p2)&((esk148_0 @ X291 @ X291)=(X291)|p2))&((f__0 @ (f__0 @ X292 @ X293) @ X294)=(f__0 @ X292 @ (f__0 @ X293 @ X294))|p2))&((esk148_0 @ (esk148_0 @ X295 @ X296) @ X297)=(esk148_0 @ X295 @ (esk148_0 @ X296 @ X297))|p2))&((f__0 @ X298 @ X299)=(f__0 @ X299 @ X298)|p2))&((esk148_0 @ X300 @ X301)=(esk148_0 @ X301 @ X300)|p2))&((f__0 @ (esk148_0 @ X302 @ X303) @ X303)=(X303)|p2))&((esk148_0 @ (f__0 @ X304 @ X305) @ X305)=(X305)|p2))&(~epred12_1 @ esk148_0|p2)), 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)],[c_0_25])])])])])])).
% 25.73/25.86 thf(c_0_32, plain, (~p45|p44), inference(fof_simplification,[status(thm)],[ax13])).
% 25.73/25.86 thf(c_0_33, plain, (p45|~p28), inference(split_conjunct,[status(thm)],[c_0_26])).
% 25.73/25.86 thf(c_0_34, plain, p28, inference(split_conjunct,[status(thm)],[ax33])).
% 25.73/25.86 thf(c_0_35, plain, (p8|~p12), inference(fof_simplification,[status(thm)],[ax43])).
% 25.73/25.86 thf(c_0_36, plain, (p5|~p8), inference(split_conjunct,[status(thm)],[c_0_27])).
% 25.73/25.86 thf(c_0_37, plain, ~p5, inference(sr,[status(thm)],[c_0_28, c_0_29])).
% 25.73/25.86 thf(c_0_38, plain, (epred11_0<=>![X1:a, X2:a, X3:a, X4:a, X5:a]:(~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((~((X3)=(X4))=>(X3)=(X5)))=>(X3)=(X1)))=>(X3)=(X2)))=>(X4)=(X5)))=>(X4)=(X1)))=>(X4)=(X2)))=>(X5)=(X1)))=>(X5)=(X2)))=>(X1)=(X2)))=>~((f__1 @ X1 @ X2)=(X2))))=>~((f__0 @ X1 @ X2)=(X1))))=>~((f__1 @ X1 @ X3)=(X3))))=>~((f__0 @ X1 @ X3)=(X1))))=>~((f__1 @ X1 @ X4)=(X4))))=>~((f__0 @ X1 @ X4)=(X1))))=>~((f__1 @ X1 @ X5)=(X5))))=>~((f__0 @ X1 @ X5)=(X1))))=>~((f__1 @ X3 @ X4)=(X2))))=>~((f__0 @ X3 @ X4)=(X1))))=>~((f__1 @ X3 @ X5)=(X3))))=>~((f__0 @ X3 @ X5)=(X5))))=>~((f__1 @ X3 @ X2)=(X2))))=>~((f__0 @ X3 @ X2)=(X3))))=>~((f__1 @ X4 @ X5)=(X2))))=>~((f__0 @ X4 @ X5)=(X1))))=>~((f__1 @ X4 @ X2)=(X2))))=>~((f__0 @ X4 @ X2)=(X4))))=>~((f__1 @ X5 @ X2)=(X2))))=>~((f__0 @ X5 @ X2)=(X5)))), introduced(definition)).
% 25.73/25.86 thf(c_0_39, plain, (~p42|((f__0 @ f__2 @ f__4)!=(f__0 @ f__4 @ f__2)|~epred4_0)), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_30])])).
% 25.73/25.86 thf(c_0_40, plain, ![X2:a, X1:a]:((f__0 @ X1 @ X2)=(f__0 @ X2 @ X1)|p2), inference(split_conjunct,[status(thm)],[c_0_31])).
% 25.73/25.86 thf(c_0_41, plain, (~p44|p18|p43), inference(fof_simplification,[status(thm)],[ax12])).
% 25.73/25.86 thf(c_0_42, plain, (p44|~p45), inference(split_conjunct,[status(thm)],[c_0_32])).
% 25.73/25.86 thf(c_0_43, plain, p45, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 25.73/25.86 thf(c_0_44, plain, (p12|~p18), inference(fof_simplification,[status(thm)],[ax37])).
% 25.73/25.86 thf(c_0_45, plain, (p8|~p12), inference(split_conjunct,[status(thm)],[c_0_35])).
% 25.73/25.86 thf(c_0_46, plain, ~p8, inference(sr,[status(thm)],[c_0_36, c_0_37])).
% 25.73/25.86 thf(c_0_47, axiom, (p3<=(~((~((~((~((~((~((~((![X1:a]:(f__0 @ X1 @ X1)=(X1)=>~(![X1:a]:(f__1 @ X1 @ X1)=(X1))))=>~(![X1:a, X2:a, X3:a]:(f__0 @ (f__0 @ X1 @ X2) @ X3)=(f__0 @ X1 @ (f__0 @ X2 @ X3)))))=>~(![X1:a, X2:a, X3:a]:(f__1 @ (f__1 @ X1 @ X2) @ X3)=(f__1 @ X1 @ (f__1 @ X2 @ X3)))))=>~(![X1:a, X2:a]:(f__0 @ X1 @ X2)=(f__0 @ X2 @ X1))))=>~(![X1:a, X2:a]:(f__1 @ X1 @ X2)=(f__1 @ X2 @ X1))))=>~(![X1:a, X2:a]:(f__0 @ (f__1 @ X1 @ X2) @ X2)=(X2))))=>~(![X1:a, X2:a]:(f__1 @ (f__0 @ X1 @ X2) @ X2)=(X2))))=>(~(epred11_0)=>~(![X1:a, X2:a, X3:a]:(f__0 @ X1 @ (f__1 @ X2 @ (f__0 @ X1 @ X3)))=(f__1 @ (f__0 @ X1 @ X2) @ (f__0 @ X1 @ X3)))))), inference(apply_def,[status(thm)],[nax3, c_0_38])).
% 25.73/25.86 thf(c_0_48, plain, (~p42|(f__0 @ f__2 @ f__4)!=(f__0 @ f__4 @ f__2)|~epred4_0), inference(split_conjunct,[status(thm)],[c_0_39])).
% 25.73/25.86 thf(c_0_49, plain, ![X2:a, X1:a]:(f__0 @ X1 @ X2)=(f__0 @ X2 @ X1), inference(sr,[status(thm)],[c_0_40, c_0_23])).
% 25.73/25.86 thf(c_0_50, plain, (~p43|p42), inference(fof_simplification,[status(thm)],[ax11])).
% 25.73/25.86 thf(c_0_51, plain, (p18|p43|~p44), inference(split_conjunct,[status(thm)],[c_0_41])).
% 25.73/25.86 thf(c_0_52, plain, p44, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 25.73/25.86 thf(c_0_53, plain, (p12|~p18), inference(split_conjunct,[status(thm)],[c_0_44])).
% 25.73/25.86 thf(c_0_54, plain, ~p12, inference(sr,[status(thm)],[c_0_45, c_0_46])).
% 25.73/25.86 thf(c_0_55, plain, ![X253:a, X254:a, X255:a, X256:a, X257:a, X258:a, X259:a, X260:a, X261:a, X262:a, X263:a, X264:a, X265:a, X266:a, X267:a, X268:a, X269:a, X270:a, X271:a]:((((((((((f__0 @ X253 @ X253)=(X253)|p3)&((f__1 @ X254 @ X254)=(X254)|p3))&((f__0 @ (f__0 @ X255 @ X256) @ X257)=(f__0 @ X255 @ (f__0 @ X256 @ X257))|p3))&((f__1 @ (f__1 @ X258 @ X259) @ X260)=(f__1 @ X258 @ (f__1 @ X259 @ X260))|p3))&((f__0 @ X261 @ X262)=(f__0 @ X262 @ X261)|p3))&((f__1 @ X263 @ X264)=(f__1 @ X264 @ X263)|p3))&((f__0 @ (f__1 @ X265 @ X266) @ X266)=(X266)|p3))&((f__1 @ (f__0 @ X267 @ X268) @ X268)=(X268)|p3))&((~epred11_0|p3)&((f__0 @ X269 @ (f__1 @ X270 @ (f__0 @ X269 @ X271)))=(f__1 @ (f__0 @ X269 @ X270) @ (f__0 @ X269 @ X271))|p3))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_47])])])])])).
% 25.73/25.86 thf(c_0_56, plain, (~p42|~epred4_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49])])).
% 25.73/25.86 thf(c_0_57, plain, (p42|~p43), inference(split_conjunct,[status(thm)],[c_0_50])).
% 25.73/25.86 thf(c_0_58, plain, (p43|p18), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 25.73/25.86 thf(c_0_59, plain, ~p18, inference(sr,[status(thm)],[c_0_53, c_0_54])).
% 25.73/25.86 thf(c_0_60, plain, ![X1:a, X2:a]:((f__0 @ (f__1 @ X1 @ X2) @ X2)=(X2)|p3), inference(split_conjunct,[status(thm)],[c_0_55])).
% 25.73/25.86 thf(c_0_61, plain, ![X356:a, X357:a, X358:a]:((~epred4_0|((X356)=(X357)|(X356)=(X358)|(X356)=(f__2)|(X356)=(f__4)|(X357)=(X358)|(X357)=(f__2)|(X357)=(f__4)|(X358)=(f__2)|(X358)=(f__4)|(f__2)=(f__4)|(f__1 @ f__2 @ f__4)!=(f__4)|(f__0 @ f__4 @ f__2)!=(f__2)|(f__1 @ f__2 @ X356)!=(X356)|(f__0 @ f__2 @ X356)!=(f__2)|(f__1 @ f__2 @ X357)!=(X357)|(f__0 @ f__2 @ X357)!=(f__2)|(f__1 @ f__2 @ X358)!=(X358)|(f__0 @ f__2 @ X358)!=(f__2)|(f__1 @ X356 @ X357)!=(f__4)|(f__0 @ X356 @ X357)!=(f__2)|(f__1 @ X356 @ X358)!=(X356)|(f__0 @ X356 @ X358)!=(X358)|(f__1 @ X356 @ f__4)!=(f__4)|(f__0 @ X356 @ f__4)!=(X356)|(f__1 @ X357 @ X358)!=(f__4)|(f__0 @ X357 @ X358)!=(f__2)|(f__1 @ X357 @ f__4)!=(f__4)|(f__0 @ X357 @ f__4)!=(X357)|(f__1 @ X358 @ f__4)!=(f__4)|(f__0 @ X358 @ f__4)!=(X358)))&(((((((((((((((((((((((((((((((esk176_0)!=(esk177_0)|epred4_0)&((esk176_0)!=(esk178_0)|epred4_0))&((esk176_0)!=(f__2)|epred4_0))&((esk176_0)!=(f__4)|epred4_0))&((esk177_0)!=(esk178_0)|epred4_0))&((esk177_0)!=(f__2)|epred4_0))&((esk177_0)!=(f__4)|epred4_0))&((esk178_0)!=(f__2)|epred4_0))&((esk178_0)!=(f__4)|epred4_0))&((f__2)!=(f__4)|epred4_0))&((f__1 @ f__2 @ f__4)=(f__4)|epred4_0))&((f__0 @ f__4 @ f__2)=(f__2)|epred4_0))&((f__1 @ f__2 @ esk176_0)=(esk176_0)|epred4_0))&((f__0 @ f__2 @ esk176_0)=(f__2)|epred4_0))&((f__1 @ f__2 @ esk177_0)=(esk177_0)|epred4_0))&((f__0 @ f__2 @ esk177_0)=(f__2)|epred4_0))&((f__1 @ f__2 @ esk178_0)=(esk178_0)|epred4_0))&((f__0 @ f__2 @ esk178_0)=(f__2)|epred4_0))&((f__1 @ esk176_0 @ esk177_0)=(f__4)|epred4_0))&((f__0 @ esk176_0 @ esk177_0)=(f__2)|epred4_0))&((f__1 @ esk176_0 @ esk178_0)=(esk176_0)|epred4_0))&((f__0 @ esk176_0 @ esk178_0)=(esk178_0)|epred4_0))&((f__1 @ esk176_0 @ f__4)=(f__4)|epred4_0))&((f__0 @ esk176_0 @ f__4)=(esk176_0)|epred4_0))&((f__1 @ esk177_0 @ esk178_0)=(f__4)|epred4_0))&((f__0 @ esk177_0 @ esk178_0)=(f__2)|epred4_0))&((f__1 @ esk177_0 @ f__4)=(f__4)|epred4_0))&((f__0 @ esk177_0 @ f__4)=(esk177_0)|epred4_0))&((f__1 @ esk178_0 @ f__4)=(f__4)|epred4_0))&((f__0 @ esk178_0 @ f__4)=(esk178_0)|epred4_0))), 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)],[c_0_24])])])])])])).
% 25.73/25.86 thf(c_0_62, plain, (~epred4_0|~p43), inference(spm,[status(thm)],[c_0_56, c_0_57])).
% 25.73/25.86 thf(c_0_63, plain, p43, inference(sr,[status(thm)],[c_0_58, c_0_59])).
% 25.73/25.86 thf(c_0_64, plain, ![X2:a, X1:a]:((f__1 @ X1 @ X2)=(f__1 @ X2 @ X1)|p3), inference(split_conjunct,[status(thm)],[c_0_55])).
% 25.73/25.86 thf(c_0_65, plain, ![X1:a, X2:a]:(f__0 @ (f__1 @ X1 @ X2) @ X2)=(X2), inference(sr,[status(thm)],[c_0_60, c_0_29])).
% 25.73/25.86 thf(c_0_66, plain, ((f__1 @ esk176_0 @ esk178_0)=(esk176_0)|epred4_0), inference(split_conjunct,[status(thm)],[c_0_61])).
% 25.73/25.86 thf(c_0_67, plain, ~epred4_0, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63])])).
% 25.73/25.86 thf(c_0_68, plain, ((f__1 @ esk176_0 @ f__4)=(f__4)|epred4_0), inference(split_conjunct,[status(thm)],[c_0_61])).
% 25.73/25.86 thf(c_0_69, plain, ![X2:a, X1:a]:(f__1 @ X1 @ X2)=(f__1 @ X2 @ X1), inference(sr,[status(thm)],[c_0_64, c_0_29])).
% 25.73/25.86 thf(c_0_70, plain, ![X1:a, X2:a, X3:a]:((f__0 @ X1 @ (f__1 @ X2 @ (f__0 @ X1 @ X3)))=(f__1 @ (f__0 @ X1 @ X2) @ (f__0 @ X1 @ X3))|p3), inference(split_conjunct,[status(thm)],[c_0_55])).
% 25.73/25.86 thf(c_0_71, plain, ![X2:a, X1:a]:(f__0 @ X1 @ (f__1 @ X2 @ X1))=(X1), inference(rw,[status(thm)],[c_0_65, c_0_49])).
% 25.73/25.86 thf(c_0_72, plain, (f__1 @ esk176_0 @ esk178_0)=(esk176_0), inference(sr,[status(thm)],[c_0_66, c_0_67])).
% 25.73/25.86 thf(c_0_73, plain, ((f__1 @ esk177_0 @ esk178_0)=(f__4)|epred4_0), inference(split_conjunct,[status(thm)],[c_0_61])).
% 25.73/25.86 thf(c_0_74, plain, ((f__1 @ f__4 @ esk176_0)=(f__4)|epred4_0), inference(rw,[status(thm)],[c_0_68, c_0_69])).
% 25.73/25.86 thf(c_0_75, plain, ![X1:a, X2:a, X3:a]:(f__1 @ (f__0 @ X1 @ X2) @ (f__0 @ X1 @ X3))=(f__0 @ X1 @ (f__1 @ X2 @ (f__0 @ X1 @ X3))), inference(sr,[status(thm)],[c_0_70, c_0_29])).
% 25.73/25.86 thf(c_0_76, plain, (f__0 @ esk176_0 @ esk178_0)=(esk178_0), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_49])).
% 25.73/25.86 thf(c_0_77, plain, ((f__0 @ esk176_0 @ esk177_0)=(f__2)|epred4_0), inference(split_conjunct,[status(thm)],[c_0_61])).
% 25.73/25.86 thf(c_0_78, plain, ((f__1 @ f__2 @ esk178_0)=(esk178_0)|epred4_0), inference(split_conjunct,[status(thm)],[c_0_61])).
% 25.73/25.86 thf(c_0_79, plain, ((f__1 @ esk178_0 @ esk177_0)=(f__4)|epred4_0), inference(rw,[status(thm)],[c_0_73, c_0_69])).
% 25.73/25.86 thf(c_0_80, plain, (f__1 @ f__4 @ esk176_0)=(f__4), inference(sr,[status(thm)],[c_0_74, c_0_67])).
% 25.73/25.86 thf(c_0_81, plain, ![X1:a]:(f__1 @ esk178_0 @ (f__0 @ esk176_0 @ X1))=(f__0 @ esk176_0 @ (f__1 @ X1 @ esk178_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_69])).
% 25.73/25.86 thf(c_0_82, plain, (f__0 @ esk176_0 @ esk177_0)=(f__2), inference(sr,[status(thm)],[c_0_77, c_0_67])).
% 25.73/25.86 thf(c_0_83, plain, (f__1 @ f__2 @ esk178_0)=(esk178_0), inference(sr,[status(thm)],[c_0_78, c_0_67])).
% 25.73/25.86 thf(c_0_84, plain, (f__1 @ esk178_0 @ esk177_0)=(f__4), inference(sr,[status(thm)],[c_0_79, c_0_67])).
% 25.73/25.86 thf(c_0_85, plain, (f__0 @ f__4 @ esk176_0)=(esk176_0), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_80]), c_0_49])).
% 25.73/25.86 thf(c_0_86, plain, (epred4_0|(esk176_0)!=(esk178_0)), inference(split_conjunct,[status(thm)],[c_0_61])).
% 25.73/25.86 thf(c_0_87, plain, (esk178_0)=(esk176_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_69]), c_0_83]), c_0_69]), c_0_84]), c_0_49]), c_0_85])).
% 25.73/25.86 thf(c_0_88, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87])]), c_0_67]), ['proof']).
% 25.73/25.86 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 25.73/25.86 thf(0,theorem,(![X1:a>a>a]:(![X2:a>a>a]:((~(((~(((~(((~(((~(((~(((~(((![X3:a]:(((X1 @ X3) @ X3) = X3)) => (~((![X3:a]:(((X2 @ X3) @ X3) = X3))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X1 @ ((X1 @ X3) @ X4)) @ X5) = ((X1 @ X3) @ ((X1 @ X4) @ X5))))))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X2 @ ((X2 @ X3) @ X4)) @ X5) = ((X2 @ X3) @ ((X2 @ X4) @ X5))))))))))) => (~((![X3:a]:(![X4:a]:(((X1 @ X3) @ X4) = ((X1 @ X4) @ X3))))))))) => (~((![X3:a]:(![X4:a]:(((X2 @ X3) @ X4) = ((X2 @ X4) @ X3))))))))) => (~((![X3:a]:(![X4:a]:(((X1 @ ((X2 @ X3) @ X4)) @ X4) = X4)))))))) => (~((![X3:a]:(![X4:a]:(((X2 @ ((X1 @ X3) @ X4)) @ X4) = X4)))))))) => ((~((![X3:a]:(![X4:a]:(![X5:a]:(![X6:a]:(![X7:a]:((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~(((~((X5 = X6))) => (X5 = X7)))) => (X5 = X3)))) => (X5 = X4)))) => (X6 = X7)))) => (X6 = X3)))) => (X6 = X4)))) => (X7 = X3)))) => (X7 = X4)))) => (X3 = X4)))) => (~((((X2 @ X3) @ X4) = X4)))))) => (~((((X1 @ X3) @ X4) = X3)))))) => (~((((X2 @ X3) @ X5) = X5)))))) => (~((((X1 @ X3) @ X5) = X3)))))) => (~((((X2 @ X3) @ X6) = X6)))))) => (~((((X1 @ X3) @ X6) = X3)))))) => (~((((X2 @ X3) @ X7) = X7)))))) => (~((((X1 @ X3) @ X7) = X3)))))) => (~((((X2 @ X5) @ X6) = X4)))))) => (~((((X1 @ X5) @ X6) = X3)))))) => (~((((X2 @ X5) @ X7) = X5)))))) => (~((((X1 @ X5) @ X7) = X7)))))) => (~((((X2 @ X5) @ X4) = X4)))))) => (~((((X1 @ X5) @ X4) = X5)))))) => (~((((X2 @ X6) @ X7) = X4)))))) => (~((((X1 @ X6) @ X7) = X3)))))) => (~((((X2 @ X6) @ X4) = X4)))))) => (~((((X1 @ X6) @ X4) = X6)))))) => (~((((X2 @ X7) @ X4) = X4)))))) => (~((((X1 @ X7) @ X4) = X7))))))))))) => (~((![X3:a]:(![X4:a]:(![X5:a]:(((X1 @ X3) @ ((X2 @ X4) @ ((X1 @ X3) @ X5))) = ((X2 @ ((X1 @ X3) @ X4)) @ ((X1 @ X3) @ X5)))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 25.73/25.86 % SZS output end Proof
%------------------------------------------------------------------------------