%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX067+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:37:51 AM UTC 2025
% Result : Theorem 0.77s 0.93s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWX067+1 : TPTP v9.1.0. Released v9.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 12:22:10 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.77/0.93 % SZS status Theorem
% 0.77/0.93 % SZS output start Proof
% 0.77/0.93 tff(eval_terminates_type, type, (
% 0.77/0.93 eval_terminates: ( $i * $i * $i ) > $o)).
% 0.77/0.93 tff(tptp_fun__0__type, type, (
% 0.77/0.93 tptp_fun__0_: $i)).
% 0.77/0.93 tff(nil_type, type, (
% 0.77/0.93 nil: $i)).
% 0.77/0.93 tff(tptp_fun_Xx2_175_type, type, (
% 0.77/0.93 tptp_fun_Xx2_175: $i)).
% 0.77/0.93 tff(tptp_fun_Xi_180_type, type, (
% 0.77/0.93 tptp_fun_Xi_180: $i)).
% 0.77/0.93 tff(tptp_fun_Xx4_54_type, type, (
% 0.77/0.93 tptp_fun_Xx4_54: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xa_172_type, type, (
% 0.77/0.93 tptp_fun_Xa_172: $i)).
% 0.77/0.93 tff(tptp_fun_Xx_179_type, type, (
% 0.77/0.93 tptp_fun_Xx_179: $i)).
% 0.77/0.93 tff(list_succeeds_type, type, (
% 0.77/0.93 list_succeeds: $i > $o)).
% 0.77/0.93 tff(cons_type, type, (
% 0.77/0.93 cons: ( $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx3_164_type, type, (
% 0.77/0.93 tptp_fun_Xx3_164: $i > $i)).
% 0.77/0.93 tff(tptp_fun_Xx2_165_type, type, (
% 0.77/0.93 tptp_fun_Xx2_165: $i > $i)).
% 0.77/0.93 tff(tptp_fun_Xx5_177_type, type, (
% 0.77/0.93 tptp_fun_Xx5_177: $i)).
% 0.77/0.93 tff(tptp_fun_Xx4_178_type, type, (
% 0.77/0.93 tptp_fun_Xx4_178: $i)).
% 0.77/0.93 tff(formula_succeeds_type, type, (
% 0.77/0.93 formula_succeeds: $i > $o)).
% 0.77/0.93 tff(and_type, type, (
% 0.77/0.93 and: ( $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx3_174_type, type, (
% 0.77/0.93 tptp_fun_Xx3_174: $i)).
% 0.77/0.93 tff(or_type, type, (
% 0.77/0.93 or: ( $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx6_176_type, type, (
% 0.77/0.93 tptp_fun_Xx6_176: $i)).
% 0.77/0.93 tff(neg_type, type, (
% 0.77/0.93 neg: $i > $i)).
% 0.77/0.93 tff(p_type, type, (
% 0.77/0.93 p: $i > $i)).
% 0.77/0.93 tff(tptp_fun_Xx7_173_type, type, (
% 0.77/0.93 tptp_fun_Xx7_173: $i)).
% 0.77/0.93 tff(tptp_fun_Xa_181_type, type, (
% 0.77/0.93 tptp_fun_Xa_181: $i)).
% 0.77/0.93 tff(tptp_fun_Xx_182_type, type, (
% 0.77/0.93 tptp_fun_Xx_182: $i)).
% 0.77/0.93 tff(tptp_fun_Xi_183_type, type, (
% 0.77/0.93 tptp_fun_Xi_183: $i)).
% 0.77/0.93 tff(literal_list_succeeds_type, type, (
% 0.77/0.93 literal_list_succeeds: $i > $o)).
% 0.77/0.93 tff(member_succeeds_type, type, (
% 0.77/0.93 member_succeeds: ( $i * $i ) > $o)).
% 0.77/0.93 tff(interpretation_succeeds_type, type, (
% 0.77/0.93 interpretation_succeeds: $i > $o)).
% 0.77/0.93 tff(tptp_fun__1__type, type, (
% 0.77/0.93 tptp_fun__1_: $i)).
% 0.77/0.93 tff(tptp_fun_Xx8_58_type, type, (
% 0.77/0.93 tptp_fun_Xx8_58: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx9_57_type, type, (
% 0.77/0.93 tptp_fun_Xx9_57: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx7_55_type, type, (
% 0.77/0.93 tptp_fun_Xx7_55: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx6_56_type, type, (
% 0.77/0.93 tptp_fun_Xx6_56: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx11_59_type, type, (
% 0.77/0.93 tptp_fun_Xx11_59: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx10_60_type, type, (
% 0.77/0.93 tptp_fun_Xx10_60: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx16_65_type, type, (
% 0.77/0.93 tptp_fun_Xx16_65: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(member_terminates_type, type, (
% 0.77/0.93 member_terminates: ( $i * $i ) > $o)).
% 0.77/0.93 tff(tptp_fun_Xx18_67_type, type, (
% 0.77/0.93 tptp_fun_Xx18_67: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx17_66_type, type, (
% 0.77/0.93 tptp_fun_Xx17_66: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(inj_185_type, type, (
% 0.77/0.93 inj_185: $i > $i)).
% 0.77/0.93 tff(tptp_fun_Xx5_53_type, type, (
% 0.77/0.93 tptp_fun_Xx5_53: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(eval_fails_type, type, (
% 0.77/0.93 eval_fails: ( $i * $i * $i ) > $o)).
% 0.77/0.93 tff(tptp_fun_Xx12_62_type, type, (
% 0.77/0.93 tptp_fun_Xx12_62: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx13_61_type, type, (
% 0.77/0.93 tptp_fun_Xx13_61: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx15_63_type, type, (
% 0.77/0.93 tptp_fun_Xx15_63: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx14_64_type, type, (
% 0.77/0.93 tptp_fun_Xx14_64: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(tptp_fun_Xx19_68_type, type, (
% 0.77/0.93 tptp_fun_Xx19_68: ( $i * $i * $i ) > $i)).
% 0.77/0.93 tff(member_fails_type, type, (
% 0.77/0.93 member_fails: ( $i * $i ) > $o)).
% 0.77/0.93 tff(incon_terminates_type, type, (
% 0.77/0.93 incon_terminates: $i > $o)).
% 0.77/0.93 tff(tptp_fun_Xx2_128_type, type, (
% 0.77/0.93 tptp_fun_Xx2_128: $i > $i)).
% 0.77/0.93 tff(tptp_fun_Xx3_166_type, type, (
% 0.77/0.93 tptp_fun_Xx3_166: $i > $i)).
% 0.77/0.93 tff(tptp_fun_Xx2_167_type, type, (
% 0.77/0.93 tptp_fun_Xx2_167: $i > $i)).
% 0.77/0.93 tff(list_fails_type, type, (
% 0.77/0.93 list_fails: $i > $o)).
% 0.77/0.93 tff(1,assumption,(~(Xi!180 = nil)), introduced(assumption)).
% 0.77/0.93 tff(2,plain,
% 0.77/0.93 (^[Xx1: $i] : refl((~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(3,plain,
% 0.77/0.94 (![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> ![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[2])).
% 0.77/0.94 tff(4,plain,
% 0.77/0.94 (^[Xx1: $i] : rewrite((~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(5,plain,
% 0.77/0.94 (![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> ![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[4])).
% 0.77/0.94 tff(6,plain,
% 0.77/0.94 (![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> ![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[5, 3])).
% 0.77/0.94 tff(7,plain,
% 0.77/0.94 (^[Xx1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1))) <=> (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1)))))), (((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) <=> ((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1)))))))), rewrite(((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1)))))) <=> ((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))), (((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) <=> ((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1)))))))), rewrite((list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))) <=> (list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))), ((((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))) <=> (((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1)))))) & (list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))), rewrite((((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1)))))) & (list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))) <=> (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))), ((((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))) <=> (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(8,plain,
% 0.77/0.94 (![Xx1: $i] : (((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))) <=> ![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[7])).
% 0.77/0.94 tff(9,plain,
% 0.77/0.94 (^[Xx1: $i] : rewrite((((~list_succeeds(Xx1)) | ((Xx1 = nil) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1))))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))) <=> (((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(10,plain,
% 0.77/0.94 (![Xx1: $i] : (((~list_succeeds(Xx1)) | ((Xx1 = nil) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1))))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))) <=> ![Xx1: $i] : (((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[9])).
% 0.77/0.94 tff(11,plain,
% 0.77/0.94 (![Xx1: $i] : (list_succeeds(Xx1) <=> ((Xx1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))) <=> ![Xx1: $i] : (list_succeeds(Xx1) <=> ((Xx1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(12,plain,
% 0.77/0.94 (^[Xx1: $i] : rewrite((list_succeeds(Xx1) <=> (?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) | (Xx1 = nil))) <=> (list_succeeds(Xx1) <=> ((Xx1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(13,plain,
% 0.77/0.94 (![Xx1: $i] : (list_succeeds(Xx1) <=> (?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) | (Xx1 = nil))) <=> ![Xx1: $i] : (list_succeeds(Xx1) <=> ((Xx1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[12])).
% 0.77/0.94 tff(14,axiom,(![Xx1: $i] : (list_succeeds(Xx1) <=> (?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) | (Xx1 = nil)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','id107')).
% 0.77/0.94 tff(15,plain,
% 0.77/0.94 (![Xx1: $i] : (list_succeeds(Xx1) <=> ((Xx1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.77/0.94 tff(16,plain,
% 0.77/0.94 (![Xx1: $i] : (list_succeeds(Xx1) <=> ((Xx1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.77/0.94 tff(17,plain,(
% 0.77/0.94 ![Xx1: $i] : (((~list_succeeds(Xx1)) | ((Xx1 = nil) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1))))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))))),
% 0.77/0.94 inference(skolemize,[status(sab)],[16])).
% 0.77/0.94 tff(18,plain,
% 0.77/0.94 (![Xx1: $i] : (((Xx1 = nil) | (~list_succeeds(Xx1)) | ((Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1))) & list_succeeds(tptp_fun_Xx3_164(Xx1)))) & (list_succeeds(Xx1) | ((~(Xx1 = nil)) & ![Xx2: $i, Xx3: $i] : (~((Xx1 = cons(Xx2, Xx3)) & list_succeeds(Xx3))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.77/0.94 tff(19,plain,
% 0.77/0.94 (![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.77/0.94 tff(20,plain,
% 0.77/0.94 (![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[19, 6])).
% 0.77/0.94 tff(21,plain,
% 0.77/0.94 (((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3)))))))))))) <=> ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3))))))))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(22,plain,
% 0.77/0.94 ((~((~((Xi!180 = nil) | (~list_succeeds(Xi!180)) | (~((~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!180))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!180 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3)))))))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(23,plain,
% 0.77/0.94 (((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((Xi!180 = nil) | (~list_succeeds(Xi!180)) | (~((~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!180))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!180 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) <=> ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3))))))))))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[22])).
% 0.77/0.94 tff(24,plain,
% 0.77/0.94 (((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((Xi!180 = nil) | (~list_succeeds(Xi!180)) | (~((~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!180))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!180 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) <=> ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3))))))))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[23, 21])).
% 0.77/0.94 tff(25,plain,
% 0.77/0.94 ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((Xi!180 = nil) | (~list_succeeds(Xi!180)) | (~((~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!180))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!180 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(26,plain,
% 0.77/0.94 ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3)))))))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.77/0.94 tff(27,plain,
% 0.77/0.94 (~((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3))))))))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[26, 20])).
% 0.77/0.94 tff(28,plain,
% 0.77/0.94 (((~((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))) | (~(list_succeeds(Xi!180) | (~((Xi!180 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!180 = cons(Xx2, Xx3)))))))))) | ((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180)))))))),
% 0.77/0.94 inference(tautology,[status(thm)],[])).
% 0.77/0.94 tff(29,plain,
% 0.77/0.94 ((~list_succeeds(Xi!180)) | (Xi!180 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!180))) | (~(Xi!180 = cons(tptp_fun_Xx2_165(Xi!180), tptp_fun_Xx3_164(Xi!180))))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.77/0.94 tff(30,assumption,(![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))), introduced(assumption)).
% 0.77/0.94 tff(31,assumption,(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))), introduced(assumption)).
% 0.77/0.94 tff(32,plain,
% 0.77/0.94 (cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)) = Xi!183),
% 0.77/0.94 inference(symmetry,[status(thm)],[31])).
% 0.77/0.94 tff(33,plain,
% 0.77/0.94 (list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))) <=> list_succeeds(Xi!183)),
% 0.77/0.94 inference(monotonicity,[status(thm)],[32])).
% 0.77/0.94 tff(34,plain,
% 0.77/0.94 (list_succeeds(Xi!183) <=> list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))),
% 0.77/0.94 inference(symmetry,[status(thm)],[33])).
% 0.77/0.94 tff(35,plain,
% 0.77/0.94 ((~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> (~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(36,plain,
% 0.77/0.94 ((~![Xa: $i] : (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)))) <=> (~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(37,axiom,(~![Xa: $i] : (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(eval:termination)'')).
% 0.77/0.94 tff(38,plain,
% 0.77/0.94 (~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.77/0.94 tff(39,plain,
% 0.77/0.94 (~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.77/0.94 tff(40,plain,
% 0.77/0.94 (~((~list_succeeds(Xi!183)) | eval_terminates(Xa!181, Xi!183, Xx!182))),
% 0.77/0.94 inference(and_elim,[status(thm)],[39])).
% 0.77/0.94 tff(41,plain,
% 0.77/0.94 (list_succeeds(Xi!183)),
% 0.77/0.94 inference(or_elim,[status(thm)],[40])).
% 0.77/0.94 tff(42,plain,
% 0.77/0.94 (list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.77/0.94 tff(43,plain,
% 0.77/0.94 (eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182) <=> eval_terminates(Xa!181, Xi!183, Xx!182)),
% 0.77/0.94 inference(monotonicity,[status(thm)],[32])).
% 0.77/0.94 tff(44,plain,
% 0.77/0.94 (eval_terminates(Xa!181, Xi!183, Xx!182) <=> eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182)),
% 0.77/0.94 inference(symmetry,[status(thm)],[43])).
% 0.77/0.94 tff(45,plain,
% 0.77/0.94 ((~eval_terminates(Xa!181, Xi!183, Xx!182)) <=> (~eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[44])).
% 0.77/0.94 tff(46,plain,
% 0.77/0.94 (~eval_terminates(Xa!181, Xi!183, Xx!182)),
% 0.77/0.94 inference(or_elim,[status(thm)],[40])).
% 0.77/0.94 tff(47,plain,
% 0.77/0.94 (~eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.77/0.94 tff(48,plain,
% 0.77/0.94 (((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | ((~list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182))) <=> ((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | (~list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(49,plain,
% 0.77/0.94 ((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | ((~list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(50,plain,
% 0.77/0.94 ((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | (~list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.77/0.94 tff(51,plain,
% 0.77/0.94 ((~list_succeeds(cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | eval_terminates(Xa!181, cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)), Xx!182)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[50, 30])).
% 0.77/0.94 tff(52,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[51, 47, 42])).
% 0.77/0.94 tff(53,plain,((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(54,plain,
% 0.77/0.94 (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[53, 30])).
% 0.77/0.94 tff(55,plain,
% 0.77/0.94 (((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))) | (Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))),
% 0.77/0.94 inference(tautology,[status(thm)],[])).
% 0.77/0.94 tff(56,plain,
% 0.77/0.94 ((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.77/0.94 tff(57,plain,
% 0.77/0.94 (((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3)))))))))))) <=> ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3))))))))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(58,plain,
% 0.77/0.94 ((~((~((Xi!183 = nil) | (~list_succeeds(Xi!183)) | (~((~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!183))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!183 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3)))))))))) <=> (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3)))))))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(59,plain,
% 0.77/0.94 (((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((Xi!183 = nil) | (~list_succeeds(Xi!183)) | (~((~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!183))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!183 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) <=> ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3))))))))))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[58])).
% 0.77/0.94 tff(60,plain,
% 0.77/0.94 (((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((Xi!183 = nil) | (~list_succeeds(Xi!183)) | (~((~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!183))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!183 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) <=> ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3))))))))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[59, 57])).
% 0.77/0.94 tff(61,plain,
% 0.77/0.94 ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((Xi!183 = nil) | (~list_succeeds(Xi!183)) | (~((~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))) | (~list_succeeds(tptp_fun_Xx3_164(Xi!183))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xi!183 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(62,plain,
% 0.77/0.94 ((~![Xx1: $i] : (~((~((Xx1 = nil) | (~list_succeeds(Xx1)) | (~((~(Xx1 = cons(tptp_fun_Xx2_165(Xx1), tptp_fun_Xx3_164(Xx1)))) | (~list_succeeds(tptp_fun_Xx3_164(Xx1))))))) | (~(list_succeeds(Xx1) | (~((Xx1 = nil) | (~![Xx2: $i, Xx3: $i] : ((~(Xx1 = cons(Xx2, Xx3))) | (~list_succeeds(Xx3))))))))))) | (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3)))))))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.77/0.94 tff(63,plain,
% 0.77/0.94 (~((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3))))))))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[62, 20])).
% 0.77/0.94 tff(64,plain,
% 0.77/0.94 (((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~(list_succeeds(Xi!183) | (~((Xi!183 = nil) | (~![Xx2: $i, Xx3: $i] : ((~list_succeeds(Xx3)) | (~(Xi!183 = cons(Xx2, Xx3)))))))))) | ((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))),
% 0.77/0.94 inference(tautology,[status(thm)],[])).
% 0.77/0.94 tff(65,plain,
% 0.77/0.94 ((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.77/0.94 tff(66,plain,
% 0.77/0.94 ((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))))),
% 0.77/0.94 inference(tautology,[status(thm)],[])).
% 0.77/0.94 tff(67,plain,
% 0.77/0.94 ((~((~list_succeeds(Xi!183)) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183)))))))) | (Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[66, 41])).
% 0.77/0.94 tff(68,plain,
% 0.77/0.94 ((Xi!183 = nil) | (~((~list_succeeds(tptp_fun_Xx3_164(Xi!183))) | (~(Xi!183 = cons(tptp_fun_Xx2_165(Xi!183), tptp_fun_Xx3_164(Xi!183))))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[67, 65])).
% 0.77/0.94 tff(69,plain,
% 0.77/0.94 (Xi!183 = nil),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[68, 56])).
% 0.77/0.94 tff(70,plain,
% 0.77/0.94 (nil = Xi!183),
% 0.77/0.94 inference(symmetry,[status(thm)],[69])).
% 0.77/0.94 tff(71,plain,
% 0.77/0.94 (eval_terminates(Xa!181, nil, Xx!182) <=> eval_terminates(Xa!181, Xi!183, Xx!182)),
% 0.77/0.94 inference(monotonicity,[status(thm)],[70])).
% 0.77/0.94 tff(72,plain,
% 0.77/0.94 (eval_terminates(Xa!181, Xi!183, Xx!182) <=> eval_terminates(Xa!181, nil, Xx!182)),
% 0.77/0.94 inference(symmetry,[status(thm)],[71])).
% 0.77/0.94 tff(73,plain,
% 0.77/0.94 ((~eval_terminates(Xa!181, Xi!183, Xx!182)) <=> (~eval_terminates(Xa!181, nil, Xx!182))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[72])).
% 0.77/0.94 tff(74,plain,
% 0.77/0.94 (~eval_terminates(Xa!181, nil, Xx!182)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[46, 73])).
% 0.77/0.94 tff(75,plain,
% 0.77/0.94 (interpretation_succeeds(nil) <=> interpretation_succeeds(nil)),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(76,axiom,(interpretation_succeeds(nil)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(interpretation:nil)'')).
% 0.77/0.94 tff(77,plain,
% 0.77/0.94 (interpretation_succeeds(nil)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.77/0.94 tff(78,plain,
% 0.77/0.94 (^[Xi: $i] : refl(((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))) <=> ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(79,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))) <=> ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[78])).
% 0.77/0.94 tff(80,plain,
% 0.77/0.94 (^[Xi: $i] : rewrite(((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))) <=> ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(81,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))) <=> ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[80])).
% 0.77/0.94 tff(82,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))) <=> ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[81, 79])).
% 0.77/0.94 tff(83,plain,
% 0.77/0.94 (^[Xi: $i] : rewrite(((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & ![Xx: $i] : (~(member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi))))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(84,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & ![Xx: $i] : (~(member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[83])).
% 0.77/0.94 tff(85,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(86,plain,
% 0.77/0.94 (^[Xi: $i] : trans(monotonicity(monotonicity(rewrite((~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))) <=> (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))), ((literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))) <=> (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))), ((interpretation_succeeds(Xi) => (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> (interpretation_succeeds(Xi) => (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))))), rewrite((interpretation_succeeds(Xi) => (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))), ((interpretation_succeeds(Xi) => (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(87,plain,
% 0.77/0.94 (![Xi: $i] : (interpretation_succeeds(Xi) => (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi))))) <=> ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[86])).
% 0.77/0.94 tff(88,axiom,(![Xi: $i] : (interpretation_succeeds(Xi) => (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(interpretation:elimination)'')).
% 0.77/0.94 tff(89,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.77/0.94 tff(90,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & (~?[Xx: $i] : (member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.77/0.94 tff(91,plain,(
% 0.77/0.94 ![Xi: $i] : ((~interpretation_succeeds(Xi)) | (literal_list_succeeds(Xi) & ![Xx: $i] : (~(member_succeeds(p(Xx), Xi) & member_succeeds(neg(p(Xx)), Xi)))))),
% 0.77/0.94 inference(skolemize,[status(sab)],[90])).
% 0.77/0.94 tff(92,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.77/0.94 tff(93,plain,
% 0.77/0.94 (![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.77/0.94 tff(94,plain,
% 0.77/0.94 (((~![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))) | ((~interpretation_succeeds(nil)) | (~((~literal_list_succeeds(nil)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), nil)) | (~member_succeeds(neg(p(Xx)), nil)))))))) <=> ((~![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))) | (~interpretation_succeeds(nil)) | (~((~literal_list_succeeds(nil)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), nil)) | (~member_succeeds(neg(p(Xx)), nil)))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(95,plain,
% 0.77/0.94 ((~![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))) | ((~interpretation_succeeds(nil)) | (~((~literal_list_succeeds(nil)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), nil)) | (~member_succeeds(neg(p(Xx)), nil)))))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(96,plain,
% 0.77/0.94 ((~![Xi: $i] : ((~interpretation_succeeds(Xi)) | (~((~literal_list_succeeds(Xi)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), Xi)) | (~member_succeeds(neg(p(Xx)), Xi)))))))) | (~interpretation_succeeds(nil)) | (~((~literal_list_succeeds(nil)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), nil)) | (~member_succeeds(neg(p(Xx)), nil))))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.77/0.94 tff(97,plain,
% 0.77/0.94 (~((~literal_list_succeeds(nil)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), nil)) | (~member_succeeds(neg(p(Xx)), nil)))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[96, 93, 77])).
% 0.77/0.94 tff(98,plain,
% 0.77/0.94 (((~literal_list_succeeds(nil)) | (~![Xx: $i] : ((~member_succeeds(p(Xx), nil)) | (~member_succeeds(neg(p(Xx)), nil))))) | literal_list_succeeds(nil)),
% 0.77/0.94 inference(tautology,[status(thm)],[])).
% 0.77/0.94 tff(99,plain,
% 0.77/0.94 (literal_list_succeeds(nil)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.77/0.94 tff(100,plain,
% 0.77/0.94 (^[Xi: $i] : refl((list_succeeds(Xi) | (~literal_list_succeeds(Xi))) <=> (list_succeeds(Xi) | (~literal_list_succeeds(Xi))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(101,plain,
% 0.77/0.95 (![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi))) <=> ![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[100])).
% 0.77/0.95 tff(102,plain,
% 0.77/0.95 (![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi))) <=> ![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(103,plain,
% 0.77/0.95 (^[Xi: $i] : rewrite((literal_list_succeeds(Xi) => list_succeeds(Xi)) <=> (list_succeeds(Xi) | (~literal_list_succeeds(Xi))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(104,plain,
% 0.77/0.95 (![Xi: $i] : (literal_list_succeeds(Xi) => list_succeeds(Xi)) <=> ![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[103])).
% 0.77/0.95 tff(105,axiom,(![Xi: $i] : (literal_list_succeeds(Xi) => list_succeeds(Xi))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(literal_list:list)'')).
% 0.77/0.95 tff(106,plain,
% 0.77/0.95 (![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.77/0.95 tff(107,plain,
% 0.77/0.95 (![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.77/0.95 tff(108,plain,(
% 0.77/0.95 ![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[107])).
% 0.77/0.95 tff(109,plain,
% 0.77/0.95 (![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.77/0.95 tff(110,plain,
% 0.77/0.95 (((~![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))) | (list_succeeds(nil) | (~literal_list_succeeds(nil)))) <=> ((~![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))) | list_succeeds(nil) | (~literal_list_succeeds(nil)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(111,plain,
% 0.77/0.95 ((~![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))) | (list_succeeds(nil) | (~literal_list_succeeds(nil)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(112,plain,
% 0.77/0.95 ((~![Xi: $i] : (list_succeeds(Xi) | (~literal_list_succeeds(Xi)))) | list_succeeds(nil) | (~literal_list_succeeds(nil))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.77/0.95 tff(113,plain,
% 0.77/0.95 (list_succeeds(nil)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[112, 109, 99])).
% 0.77/0.95 tff(114,plain,
% 0.77/0.95 (((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | ((~list_succeeds(nil)) | eval_terminates(Xa!181, nil, Xx!182))) <=> ((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | (~list_succeeds(nil)) | eval_terminates(Xa!181, nil, Xx!182))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(115,plain,
% 0.77/0.95 ((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | ((~list_succeeds(nil)) | eval_terminates(Xa!181, nil, Xx!182))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(116,plain,
% 0.77/0.95 ((~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))) | (~list_succeeds(nil)) | eval_terminates(Xa!181, nil, Xx!182)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.77/0.95 tff(117,plain,
% 0.77/0.95 (eval_terminates(Xa!181, nil, Xx!182)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[116, 113, 30])).
% 0.77/0.95 tff(118,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[117, 74])).
% 0.77/0.95 tff(119,plain,(~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(120,assumption,(~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))), introduced(assumption)).
% 0.77/0.95 tff(121,plain,
% 0.77/0.95 (formula_succeeds(Xa!181)),
% 0.77/0.95 inference(and_elim,[status(thm)],[39])).
% 0.77/0.95 tff(122,assumption,(![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), introduced(assumption)).
% 0.77/0.95 tff(123,plain,
% 0.77/0.95 (((~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ((~formula_succeeds(Xa!181)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx)))) <=> ((~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | (~formula_succeeds(Xa!181)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(124,plain,
% 0.77/0.95 ((~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ((~formula_succeeds(Xa!181)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(125,plain,
% 0.77/0.95 ((~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | (~formula_succeeds(Xa!181)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.77/0.95 tff(126,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[125, 122, 121, 120])).
% 0.77/0.95 tff(127,plain,((~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa!181, Xi, Xx))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(128,plain,
% 0.77/0.95 (~![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[127, 119])).
% 0.77/0.95 tff(129,plain,
% 0.77/0.95 (((~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179) | (~((Xa!172 = p(Xx7!173)) | (~((~(Xa!172 = or(Xx2!175, Xx3!174))) | (~formula_succeeds(Xx2!175)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx))) | (~formula_succeeds(Xx3!174)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))))) | (~((~(Xa!172 = neg(Xx6!176))) | (~formula_succeeds(Xx6!176)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))))) | (~((~(Xa!172 = and(Xx4!178, Xx5!177))) | (~formula_succeeds(Xx4!178)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx))) | (~formula_succeeds(Xx5!177)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx))))))))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> ((~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179) | (~((Xa!172 = p(Xx7!173)) | (~((~(Xa!172 = neg(Xx6!176))) | (~formula_succeeds(Xx6!176)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))))) | (~((~(Xa!172 = or(Xx2!175, Xx3!174))) | (~formula_succeeds(Xx2!175)) | (~formula_succeeds(Xx3!174)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx))) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))))) | (~((~(Xa!172 = and(Xx4!178, Xx5!177))) | (~formula_succeeds(Xx4!178)) | (~formula_succeeds(Xx5!177)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx))) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx))))))))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(130,plain,
% 0.77/0.95 (((~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179) | (~((Xa!172 = p(Xx7!173)) | (~((~(Xa!172 = or(Xx2!175, Xx3!174))) | (~formula_succeeds(Xx2!175)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx))) | (~formula_succeeds(Xx3!174)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))))) | (~((~(Xa!172 = neg(Xx6!176))) | (~formula_succeeds(Xx6!176)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))))) | (~((~(Xa!172 = and(Xx4!178, Xx5!177))) | (~formula_succeeds(Xx4!178)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx))) | (~formula_succeeds(Xx5!177)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx))))))))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> ((~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179) | (~((Xa!172 = p(Xx7!173)) | (~((~(Xa!172 = or(Xx2!175, Xx3!174))) | (~formula_succeeds(Xx2!175)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx))) | (~formula_succeeds(Xx3!174)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))))) | (~((~(Xa!172 = neg(Xx6!176))) | (~formula_succeeds(Xx6!176)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))))) | (~((~(Xa!172 = and(Xx4!178, Xx5!177))) | (~formula_succeeds(Xx4!178)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx))) | (~formula_succeeds(Xx5!177)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx))))))))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(131,plain,
% 0.77/0.95 (((((Xa!172 = p(Xx7!173)) | ((Xa!172 = or(Xx2!175, Xx3!174)) & formula_succeeds(Xx2!175) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx)) & formula_succeeds(Xx3!174) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))) | ((Xa!172 = neg(Xx6!176)) & formula_succeeds(Xx6!176) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))) | ((Xa!172 = and(Xx4!178, Xx5!177)) & formula_succeeds(Xx4!178) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx)) & formula_succeeds(Xx5!177) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx)))) & (~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> ((~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179) | (~((Xa!172 = p(Xx7!173)) | (~((~(Xa!172 = or(Xx2!175, Xx3!174))) | (~formula_succeeds(Xx2!175)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx))) | (~formula_succeeds(Xx3!174)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))))) | (~((~(Xa!172 = neg(Xx6!176))) | (~formula_succeeds(Xx6!176)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))))) | (~((~(Xa!172 = and(Xx4!178, Xx5!177))) | (~formula_succeeds(Xx4!178)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx))) | (~formula_succeeds(Xx5!177)) | (~![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx))))))))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(132,plain,
% 0.77/0.95 ((((Xa!172 = p(Xx7!173)) | ((Xa!172 = or(Xx2!175, Xx3!174)) & formula_succeeds(Xx2!175) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx)) & formula_succeeds(Xx3!174) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))) | ((Xa!172 = neg(Xx6!176)) & formula_succeeds(Xx6!176) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))) | ((Xa!172 = and(Xx4!178, Xx5!177)) & formula_succeeds(Xx4!178) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx)) & formula_succeeds(Xx5!177) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx)))) & (~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179)))) <=> (((Xa!172 = p(Xx7!173)) | ((Xa!172 = or(Xx2!175, Xx3!174)) & formula_succeeds(Xx2!175) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx)) & formula_succeeds(Xx3!174) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))) | ((Xa!172 = neg(Xx6!176)) & formula_succeeds(Xx6!176) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))) | ((Xa!172 = and(Xx4!178, Xx5!177)) & formula_succeeds(Xx4!178) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx)) & formula_succeeds(Xx5!177) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx)))) & (~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(133,plain,
% 0.77/0.95 (((((Xa!172 = p(Xx7!173)) | ((Xa!172 = or(Xx2!175, Xx3!174)) & formula_succeeds(Xx2!175) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx)) & formula_succeeds(Xx3!174) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))) | ((Xa!172 = neg(Xx6!176)) & formula_succeeds(Xx6!176) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))) | ((Xa!172 = and(Xx4!178, Xx5!177)) & formula_succeeds(Xx4!178) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx)) & formula_succeeds(Xx5!177) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx)))) & (~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> ((((Xa!172 = p(Xx7!173)) | ((Xa!172 = or(Xx2!175, Xx3!174)) & formula_succeeds(Xx2!175) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2!175, Xi, Xx)) & formula_succeeds(Xx3!174) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3!174, Xi, Xx))) | ((Xa!172 = neg(Xx6!176)) & formula_succeeds(Xx6!176) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6!176, Xi, Xx))) | ((Xa!172 = and(Xx4!178, Xx5!177)) & formula_succeeds(Xx4!178) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4!178, Xi, Xx)) & formula_succeeds(Xx5!177) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5!177, Xi, Xx)))) & (~((~list_succeeds(Xi!180)) | eval_terminates(Xa!172, Xi!180, Xx!179)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[132])).
% 0.77/0.95 tff(134,plain,
% 0.77/0.95 (((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(135,plain,
% 0.77/0.95 ((![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))) => ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) <=> ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(136,plain,
% 0.77/0.95 (^[Xa: $i] : trans(monotonicity(quant_intro(proof_bind(^[Xi: $i, Xx: $i] : rewrite((list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)) <=> ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), (![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)) <=> ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), ((formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) <=> (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))), rewrite((formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))) <=> ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), ((formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) <=> ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(137,plain,
% 0.77/0.95 (![Xa: $i] : (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) <=> ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[136])).
% 0.77/0.95 tff(138,plain,
% 0.77/0.95 (^[Xa: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) <=> (?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))), quant_intro(proof_bind(^[Xx6: $i] : trans(monotonicity(quant_intro(proof_bind(^[Xi: $i, Xx: $i] : rewrite((list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)) <=> ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx)))), (![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)) <=> ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx)))), ((((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx))) <=> (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))))), rewrite((((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) <=> ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx)))), ((((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx))) <=> ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx)))))), (?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx))) <=> ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))))), (((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) <=> ((?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx)))))), rewrite(((?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx)))) <=> (?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))), (((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) <=> (?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))))), ((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) <=> ((?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))))), rewrite(((?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) <=> (?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))), ((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) <=> (?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))))), quant_intro(proof_bind(^[Xi: $i, Xx: $i] : rewrite((list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)) <=> ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), (![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)) <=> ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), (((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) <=> ((?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))) => ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))), rewrite(((?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx)))) => ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))) <=> ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))), (((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) <=> ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(139,plain,
% 0.77/0.95 (![Xa: $i] : ((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) <=> ![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[138])).
% 0.77/0.95 tff(140,plain,
% 0.77/0.95 ((![Xa: $i] : ((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) => ![Xa: $i] : (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)))) <=> (![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))) => ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[139, 137])).
% 0.77/0.96 tff(141,plain,
% 0.77/0.96 ((![Xa: $i] : ((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) => ![Xa: $i] : (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)))) <=> ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx))))),
% 0.77/0.96 inference(transitivity,[status(thm)],[140, 135])).
% 0.77/0.96 tff(142,axiom,(![Xa: $i] : ((((?[Xx2: $i, Xx3: $i] : (((((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx2, Xi, Xx))) & formula_succeeds(Xx3)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx3, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : (((((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx4, Xi, Xx))) & formula_succeeds(Xx5)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx5, Xi, Xx)))) | ?[Xx6: $i] : (((Xa = neg(Xx6)) & formula_succeeds(Xx6)) & ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xx6, Xi, Xx)))) | ?[Xx7: $i] : (Xa = p(Xx7))) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx))) => ![Xa: $i] : (formula_succeeds(Xa) => ![Xi: $i, Xx: $i] : (list_succeeds(Xi) => eval_terminates(Xa, Xi, Xx)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','induction')).
% 0.77/0.96 tff(143,plain,
% 0.77/0.96 ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.77/0.96 tff(144,plain,
% 0.77/0.96 ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[143, 134])).
% 0.77/0.96 tff(145,plain,
% 0.77/0.96 ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.77/0.96 tff(146,plain,
% 0.77/0.96 ((~![Xa: $i] : ((~(?[Xx7: $i] : (Xa = p(Xx7)) | ?[Xx2: $i, Xx3: $i] : ((Xa = or(Xx2, Xx3)) & formula_succeeds(Xx2) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx2, Xi, Xx)) & formula_succeeds(Xx3) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx3, Xi, Xx))) | ?[Xx6: $i] : ((Xa = neg(Xx6)) & formula_succeeds(Xx6) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx6, Xi, Xx))) | ?[Xx4: $i, Xx5: $i] : ((Xa = and(Xx4, Xx5)) & formula_succeeds(Xx4) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx4, Xi, Xx)) & formula_succeeds(Xx5) & ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xx5, Xi, Xx))))) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))) | ![Xa: $i] : ((~formula_succeeds(Xa)) | ![Xi: $i, Xx: $i] : ((~list_succeeds(Xi)) | eval_terminates(Xa, Xi, Xx)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[145, 134])).
% 0.77/0.96 Proof display could not be completed: monotonicity rule is not handled
% 0.77/0.97 % E exiting
%------------------------------------------------------------------------------