0.07/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.keOEXvb3VW 0.12/0.32 % Computer : n024.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 960 0.12/0.32 % DateTime : Thu Jul 2 08:31:11 EDT 2020 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 120 s 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.33 % Number of cores: 8 0.12/0.33 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.18/0.50 % Estimated wc time : 1286 0.18/0.50 % Estimated cpu time (7 cpus) : 183.71428571428572 0.56/0.59 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.56/0.59 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.56/0.60 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.56/0.61 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.95/0.65 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.95/0.65 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.97/0.71 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 23.58/4.00 % Solved by lams/c.easy.sh. 23.58/4.00 % Running : timeout 10 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.keOEXvb3VW/e_inputc9f8e7 --cpu-limit=8 --auto -s -p. 23.58/4.00 % done 946 iterations in 3.281s 23.58/4.00 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 23.58/4.00 % SZS output start Refutation 23.58/4.00 tff(hoaslaminj_gthm, axiom, hoaslaminj_gthm <=> 23.58/4.00 (axapp => 23.58/4.00 (axvarcons => 23.58/4.00 (axvarid => 23.58/4.00 (axabs => 23.58/4.00 (axclos => 23.58/4.00 (axidl => 23.58/4.00 (axshiftcons => 23.58/4.00 (axassoc => 23.58/4.00 (axmap => 23.58/4.00 (axidr => 23.58/4.00 (axvarshift => 23.58/4.00 (axscons => 23.58/4.00 (ulamvar1 => 23.58/4.00 (ulamvarsh => 23.58/4.00 (ulamvarind => 23.58/4.00 (apinj1 => 23.58/4.00 (apinj2 => 23.58/4.00 (laminj => 23.58/4.00 (shinj => 23.58/4.00 (lamnotap => 23.58/4.00 (apnotvar => 23.58/4.00 (lamnotvar => 23.58/4.00 (induction => 23.58/4.00 (pushprop => 23.58/4.00 (induction2lem => 23.58/4.00 (induction2 => 23.58/4.00 (substmonoid => 23.58/4.00 (termmset => 23.58/4.00 (hoasapinj1 => (hoasapinj2 => hoaslaminj))))))))))))))))))))))))))))))). 23.58/4.00 tff('0', plain, 23.58/4.00 hoaslaminj_gthm = 23.58/4.00 (axapp => 23.58/4.00 (axvarcons => 23.58/4.00 (axvarid => 23.58/4.00 (axabs => 23.58/4.00 (axclos => 23.58/4.00 (axidl => 23.58/4.00 (axshiftcons => 23.58/4.00 (axassoc => 23.58/4.00 (axmap => 23.58/4.00 (axidr => 23.58/4.00 (axvarshift => 23.58/4.00 (axscons => 23.58/4.00 (ulamvar1 => 23.58/4.00 (ulamvarsh => 23.58/4.00 (ulamvarind => 23.58/4.00 (apinj1 => 23.58/4.00 (apinj2 => 23.58/4.00 (laminj => 23.58/4.00 (shinj => 23.58/4.00 (lamnotap => 23.58/4.00 (apnotvar => 23.58/4.00 (lamnotvar => 23.58/4.00 (induction => 23.58/4.00 (pushprop => 23.58/4.00 (induction2lem => 23.58/4.00 (induction2 => 23.58/4.00 (substmonoid => 23.58/4.00 (termmset => 23.58/4.00 (hoasapinj1 => (hoasapinj2 => hoaslaminj)))))))))))))))))))))))))))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(hoaslaminj, axiom, hoaslaminj <=> 23.58/4.00 (![F:((subst * term) > term)]: 23.58/4.00 ((![M:subst,A:term,N:subst]: (sub(F(M,A),N) = F(comp(M,N),sub(A,N)))) => 23.58/4.00 (![G:((subst * term) > term)]: 23.58/4.00 ((![M:subst,A:term,N:subst]: (sub(G(M,A),N) = G(comp(M,N),sub(A,N)))) => 23.58/4.00 ((hoaslam(id,^[M:subst,A:term]: F(M,A)) = 23.58/4.00 hoaslam(id,^[M:subst,A:term]: G(M,A))) => 23.58/4.00 (![M:subst,A:term]: (F(M,A) = G(M,A))))))))). 23.58/4.00 tff('1', plain, 23.58/4.00 hoaslaminj = 23.58/4.00 (![X4:((subst * term) > term)]: 23.58/4.00 ((![X6:subst,X8:term,X10:subst]: 23.58/4.00 (sub(X4(X6,X8),X10) = X4(comp(X6,X10),sub(X8,X10)))) => 23.58/4.00 (![X12:((subst * term) > term)]: 23.58/4.00 ((![X14:subst,X16:term,X18:subst]: 23.58/4.00 (sub(X12(X14,X16),X18) = X12(comp(X14,X18),sub(X16,X18)))) => 23.58/4.00 ((hoaslam(id,^[V_1:subst,V_2:term]: X4(V_1,V_2)) = 23.58/4.00 hoaslam(id,^[V_3:subst,V_4:term]: X12(V_3,V_4))) => 23.58/4.00 (![X20:subst,X22:term]: (X4(X20,X22) = X12(X20,X22)))))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(hoasapinj2, axiom, hoasapinj2 <=> 23.58/4.00 (![A:term,B:term,C:term,D:term]: 23.58/4.00 ((hoasap(id,A,id,C) = hoasap(id,B,id,D)) => (C = D)))). 23.58/4.00 tff('2', plain, 23.58/4.00 hoasapinj2 = 23.58/4.00 (![X4:term,X6:term,X8:term,X10:term]: 23.58/4.00 ((hoasap(id,X4,id,X8) = hoasap(id,X6,id,X10)) => (X8 = X10))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(hoasapinj1, axiom, hoasapinj1 <=> 23.58/4.00 (![A:term,B:term,C:term,D:term]: 23.58/4.00 ((hoasap(id,A,id,C) = hoasap(id,B,id,D)) => (A = B)))). 23.58/4.00 tff('3', plain, 23.58/4.00 hoasapinj1 = 23.58/4.00 (![X4:term,X6:term,X8:term,X10:term]: 23.58/4.00 ((hoasap(id,X4,id,X8) = hoasap(id,X6,id,X10)) => (X4 = X6))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(hoaslam, axiom, hoaslam() = 23.58/4.00 ^[M:subst,F:((subst * term) > term)]: lam(F(sh,one))). 23.58/4.00 tff('4', plain, 23.58/4.00 hoaslam = (^[M:subst,F:((subst * term) > term)]: lam(F(sh,one))), 23.58/4.00 inference('simplify_rw_rule', [status(thm)], [hoaslam])). 23.58/4.00 tff('5', plain, 23.58/4.00 hoaslam = (^[V_1:subst,V_2:((subst * term) > term)]: lam(V_2(sh,one))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(hoasap, axiom, hoasap() = 23.58/4.00 ^[M:subst,A:term,N:subst,B:term]: ap(sub(A,N),B)). 23.58/4.00 tff('6', plain, hoasap = (^[M:subst,A:term,N:subst,B:term]: ap(sub(A,N),B)), 23.58/4.00 inference('simplify_rw_rule', [status(thm)], [hoasap])). 23.58/4.00 tff('7', plain, 23.58/4.00 hoasap = (^[V_1:subst,V_2:term,V_3:subst,V_4:term]: ap(sub(V_2,V_3),V_4)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(termmset, axiom, termmset <=> 23.58/4.00 ((![A:term]: (sub(A,id) = A)) & 23.58/4.00 (![A:term,M:subst,N:subst]: (sub(sub(A,M),N) = sub(A,comp(M,N)))))). 23.58/4.00 tff('8', plain, 23.58/4.00 termmset = 23.58/4.00 ((![X4:term]: (sub(X4,id) = X4)) & 23.58/4.00 (![X6:term,X8:subst,X10:subst]: 23.58/4.00 (sub(sub(X6,X8),X10) = sub(X6,comp(X8,X10))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(substmonoid, axiom, substmonoid <=> 23.58/4.00 ((![M:subst]: (comp(M,id) = M)) & (![M:subst]: (comp(id,M) = M)) & 23.58/4.00 (![M:subst,N:subst,K:subst]: (comp(comp(M,N),K) = comp(M,comp(N,K)))))). 23.58/4.00 tff('9', plain, 23.58/4.00 substmonoid = 23.58/4.00 ((![X4:subst]: (comp(X4,id) = X4)) & (![X6:subst]: (comp(id,X6) = X6)) & 23.58/4.00 (![X8:subst,X10:subst,X12:subst]: 23.58/4.00 (comp(comp(X8,X10),X12) = comp(X8,comp(X10,X12))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(induction2, axiom, induction2 <=> 23.58/4.00 (![P:((term > $o))]: 23.58/4.00 ((![A:term]: (var(A) => P(A))) => 23.58/4.00 ((![A:term,B:term]: (P(A) => (P(B) => P(ap(A,B))))) => 23.58/4.00 ((![A:term]: 23.58/4.00 ((![B:term]: (P(B) => P(sub(A,push(B,id))))) => P(lam(A)))) => 23.58/4.00 (![A:term]: P(A))))))). 23.58/4.00 tff('10', plain, 23.58/4.00 induction2 = 23.58/4.00 (![X4:((term > $o))]: 23.58/4.00 ((![X6:term]: (var(X6) => X4(X6))) => 23.58/4.00 ((![X8:term,X10:term]: (X4(X8) => (X4(X10) => X4(ap(X8,X10))))) => 23.58/4.00 ((![X12:term]: 23.58/4.00 ((![X14:term]: (X4(X14) => X4(sub(X12,push(X14,id))))) => 23.58/4.00 X4(lam(X12)))) => 23.58/4.00 (![X16:term]: X4(X16)))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(induction2lem, axiom, induction2lem <=> 23.58/4.00 (![P:((term > $o))]: 23.58/4.00 ((![A:term,B:term]: (P(A) => (P(B) => P(ap(A,B))))) => 23.58/4.00 ((![A:term]: ((![B:term]: (P(B) => P(sub(A,push(B,id))))) => P(lam(A)))) => 23.58/4.00 (![A:term,M:subst]: 23.58/4.00 ((![B:term]: (var(B) => P(sub(B,M)))) => P(sub(A,M)))))))). 23.58/4.00 tff('11', plain, 23.58/4.00 induction2lem = 23.58/4.00 (![X4:((term > $o))]: 23.58/4.00 ((![X6:term,X8:term]: (X4(X6) => (X4(X8) => X4(ap(X6,X8))))) => 23.58/4.00 ((![X10:term]: 23.58/4.00 ((![X12:term]: (X4(X12) => X4(sub(X10,push(X12,id))))) => 23.58/4.00 X4(lam(X10)))) => 23.58/4.00 (![X14:term,X16:subst]: 23.58/4.00 ((![X18:term]: (var(X18) => X4(sub(X18,X16)))) => 23.58/4.00 X4(sub(X14,X16))))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(pushprop, axiom, pushprop <=> 23.58/4.00 (![P:((term > $o)),A:term,M:subst]: 23.58/4.00 ((![B:term]: (var(B) => P(sub(B,M)))) => 23.58/4.00 (P(A) => (![B:term]: (var(B) => P(sub(B,push(A,M))))))))). 23.58/4.00 tff('12', plain, 23.58/4.00 pushprop = 23.58/4.00 (![X4:((term > $o)),X6:term,X8:subst]: 23.58/4.00 ((![X10:term]: (var(X10) => X4(sub(X10,X8)))) => 23.58/4.00 (X4(X6) => (![X12:term]: (var(X12) => X4(sub(X12,push(X6,X8)))))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(induction, axiom, induction <=> 23.58/4.00 (![P:((term > $o))]: 23.58/4.00 ((![A:term]: (var(A) => P(A))) => 23.58/4.00 ((![A:term,B:term]: (P(A) => (P(B) => P(ap(A,B))))) => 23.58/4.00 ((![A:term]: (P(A) => P(lam(A)))) => (![A:term]: P(A))))))). 23.58/4.00 tff('13', plain, 23.58/4.00 induction = 23.58/4.00 (![X4:((term > $o))]: 23.58/4.00 ((![X6:term]: (var(X6) => X4(X6))) => 23.58/4.00 ((![X8:term,X10:term]: (X4(X8) => (X4(X10) => X4(ap(X8,X10))))) => 23.58/4.00 ((![X12:term]: (X4(X12) => X4(lam(X12)))) => (![X14:term]: X4(X14)))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(lamnotvar, axiom, lamnotvar <=> (![A:term]: (~var(lam(A))))). 23.58/4.00 tff('14', plain, lamnotvar = (![X4:term]: (~var(lam(X4)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(apnotvar, axiom, apnotvar <=> (![A:term,B:term]: (~var(ap(A,B))))). 23.58/4.00 tff('15', plain, apnotvar = (![X4:term,X6:term]: (~var(ap(X4,X6)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(lamnotap, axiom, lamnotap <=> 23.58/4.00 (![A:term,B:term,C:term]: (lam(A) != ap(B,C)))). 23.58/4.00 tff('16', plain, 23.58/4.00 lamnotap = (![X4:term,X6:term,X8:term]: (lam(X4) != ap(X6,X8))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(shinj, axiom, shinj <=> 23.58/4.00 (![A:term,B:term]: ((sub(A,sh) = sub(B,sh)) => (A = B)))). 23.58/4.00 tff('17', plain, 23.58/4.00 shinj = (![X4:term,X6:term]: ((sub(X4,sh) = sub(X6,sh)) => (X4 = X6))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(laminj, axiom, laminj <=> 23.58/4.00 (![A:term,B:term]: ((lam(A) = lam(B)) => (A = B)))). 23.58/4.00 tff('18', plain, 23.58/4.00 laminj = (![X4:term,X6:term]: ((lam(X4) = lam(X6)) => (X4 = X6))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(apinj2, axiom, apinj2 <=> 23.58/4.00 (![A:term,B:term,C:term,D:term]: ((ap(A,C) = ap(B,D)) => (C = D)))). 23.58/4.00 tff('19', plain, 23.58/4.00 apinj2 = 23.58/4.00 (![X4:term,X6:term,X8:term,X10:term]: 23.58/4.00 ((ap(X4,X8) = ap(X6,X10)) => (X8 = X10))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(apinj1, axiom, apinj1 <=> 23.58/4.00 (![A:term,B:term,C:term,D:term]: ((ap(A,C) = ap(B,D)) => (A = B)))). 23.58/4.00 tff('20', plain, 23.58/4.00 apinj1 = 23.58/4.00 (![X4:term,X6:term,X8:term,X10:term]: 23.58/4.00 ((ap(X4,X8) = ap(X6,X10)) => (X4 = X6))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(ulamvarind, axiom, ulamvarind <=> 23.58/4.00 (![P:((term > $o))]: 23.58/4.00 (P(one) => 23.58/4.00 ((![A:term]: (var(A) => (P(A) => P(sub(A,sh))))) => 23.58/4.00 (![A:term]: (var(A) => P(A))))))). 23.58/4.00 tff('21', plain, 23.58/4.00 ulamvarind = 23.58/4.00 (![X4:((term > $o))]: 23.58/4.00 (X4(one) => 23.58/4.00 ((![X6:term]: (var(X6) => (X4(X6) => X4(sub(X6,sh))))) => 23.58/4.00 (![X8:term]: (var(X8) => X4(X8)))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(ulamvarsh, axiom, ulamvarsh <=> (![A:term]: (var(A) => var(sub(A,sh))))). 23.58/4.00 tff('22', plain, ulamvarsh = (![X4:term]: (var(X4) => var(sub(X4,sh)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(ulamvar1, axiom, ulamvar1() = var(one)). 23.58/4.00 tff('23', plain, ulamvar1 = var(one), 23.58/4.00 inference('simplify_rw_rule', [status(thm)], [ulamvar1])). 23.58/4.00 tff('24', plain, ulamvar1 = var(one), define([status(thm)])). 23.58/4.00 tff(axscons, axiom, axscons <=> 23.58/4.00 (![M:subst]: (push(sub(one,M),comp(sh,M)) = M))). 23.58/4.00 tff('25', plain, 23.58/4.00 axscons = (![X4:subst]: (push(sub(one,X4),comp(sh,X4)) = X4)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axvarshift, axiom, axvarshift <=> (push(one,sh) = id)). 23.58/4.00 tff('26', plain, axvarshift = (push(one,sh) = id), define([status(thm)])). 23.58/4.00 tff(axidr, axiom, axidr <=> (![M:subst]: (comp(M,id) = M))). 23.58/4.00 tff('27', plain, axidr = (![X4:subst]: (comp(X4,id) = X4)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axmap, axiom, axmap <=> 23.58/4.00 (![A:term,M:subst,N:subst]: (comp(push(A,M),N) = push(sub(A,N),comp(M,N))))). 23.58/4.00 tff('28', plain, 23.58/4.00 axmap = 23.58/4.00 (![X4:term,X6:subst,X8:subst]: 23.58/4.00 (comp(push(X4,X6),X8) = push(sub(X4,X8),comp(X6,X8)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axassoc, axiom, axassoc <=> 23.58/4.00 (![M:subst,N:subst,K:subst]: (comp(comp(M,N),K) = comp(M,comp(N,K))))). 23.58/4.00 tff('29', plain, 23.58/4.00 axassoc = 23.58/4.00 (![X4:subst,X6:subst,X8:subst]: 23.58/4.00 (comp(comp(X4,X6),X8) = comp(X4,comp(X6,X8)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axshiftcons, axiom, axshiftcons <=> 23.58/4.00 (![A:term,M:subst]: (comp(sh,push(A,M)) = M))). 23.58/4.00 tff('30', plain, 23.58/4.00 axshiftcons = (![X4:term,X6:subst]: (comp(sh,push(X4,X6)) = X6)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axidl, axiom, axidl <=> (![M:subst]: (comp(id,M) = M))). 23.58/4.00 tff('31', plain, axidl = (![X4:subst]: (comp(id,X4) = X4)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axclos, axiom, axclos <=> 23.58/4.00 (![A:term,M:subst,N:subst]: (sub(sub(A,M),N) = sub(A,comp(M,N))))). 23.58/4.00 tff('32', plain, 23.58/4.00 axclos = 23.58/4.00 (![X4:term,X6:subst,X8:subst]: (sub(sub(X4,X6),X8) = sub(X4,comp(X6,X8)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axabs, axiom, axabs <=> 23.58/4.00 (![A:term,M:subst]: (sub(lam(A),M) = lam(sub(A,push(one,comp(M,sh))))))). 23.58/4.00 tff('33', plain, 23.58/4.00 axabs = 23.58/4.00 (![X4:term,X6:subst]: 23.58/4.00 (sub(lam(X4),X6) = lam(sub(X4,push(one,comp(X6,sh)))))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axvarid, axiom, axvarid <=> (![A:term]: (sub(A,id) = A))). 23.58/4.00 tff('34', plain, axvarid = (![X4:term]: (sub(X4,id) = X4)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axvarcons, axiom, axvarcons <=> 23.58/4.00 (![A:term,M:subst]: (sub(one,push(A,M)) = A))). 23.58/4.00 tff('35', plain, 23.58/4.00 axvarcons = (![X4:term,X6:subst]: (sub(one,push(X4,X6)) = X4)), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(axapp, axiom, axapp <=> 23.58/4.00 (![A:term,B:term,M:subst]: (sub(ap(A,B),M) = ap(sub(A,M),sub(B,M))))). 23.58/4.00 tff('36', plain, 23.58/4.00 axapp = 23.58/4.00 (![X4:term,X6:term,X8:subst]: 23.58/4.00 (sub(ap(X4,X6),X8) = ap(sub(X4,X8),sub(X6,X8)))), 23.58/4.00 define([status(thm)])). 23.58/4.00 tff(thm, conjecture, (hoaslaminj_gthm)). 23.58/4.00 tff(zf_stmt_0, conjecture, 23.58/4.00 ((![X4:term,X6:term,X8:subst]: 23.58/4.00 (sub(ap(X4,X6),X8) = ap(sub(X4,X8),sub(X6,X8)))) => 23.58/4.00 ((![X10:term,X12:subst]: (sub(one,push(X10,X12)) = X10)) => 23.58/4.00 ((![X14:term]: (sub(X14,id) = X14)) => 23.58/4.00 ((![X16:term,X18:subst]: 23.58/4.00 (sub(lam(X16),X18) = lam(sub(X16,push(one,comp(X18,sh)))))) => 23.58/4.00 ((![X20:term,X22:subst,X24:subst]: 23.58/4.00 (sub(sub(X20,X22),X24) = sub(X20,comp(X22,X24)))) => 23.58/4.00 ((![X26:subst]: (comp(id,X26) = X26)) => 23.58/4.00 ((![X28:term,X30:subst]: (comp(sh,push(X28,X30)) = X30)) => 23.58/4.00 ((![X32:subst,X34:subst,X36:subst]: 23.58/4.00 (comp(comp(X32,X34),X36) = comp(X32,comp(X34,X36)))) => 23.58/4.00 ((![X38:term,X40:subst,X42:subst]: 23.58/4.00 (comp(push(X38,X40),X42) = push(sub(X38,X42),comp(X40,X42)))) => 23.58/4.00 ((![X44:subst]: (comp(X44,id) = X44)) => 23.58/4.00 ((push(one,sh) = id) => 23.58/4.00 ((![X46:subst]: (push(sub(one,X46),comp(sh,X46)) = X46)) => 23.58/4.00 (var(one) => 23.58/4.00 ((![X48:term]: (var(X48) => var(sub(X48,sh)))) => 23.58/4.00 ((![X50:((term > $o))]: 23.58/4.00 (X50(one) => 23.58/4.00 ((![X52:term]: 23.58/4.00 (var(X52) => (X50(X52) => X50(sub(X52,sh))))) => 23.58/4.00 (![X54:term]: (var(X54) => X50(X54)))))) => 23.58/4.00 ((![X56:term,X58:term,X60:term,X62:term]: 23.58/4.00 ((ap(X56,X60) = ap(X58,X62)) => (X56 = X58))) => 23.58/4.00 ((![X64:term,X66:term,X68:term,X70:term]: 23.58/4.00 ((ap(X64,X68) = ap(X66,X70)) => (X68 = X70))) => 23.58/4.00 ((![X72:term,X74:term]: 23.58/4.00 ((lam(X72) = lam(X74)) => (X72 = X74))) => 23.58/4.00 ((![X76:term,X78:term]: 23.58/4.00 ((sub(X76,sh) = sub(X78,sh)) => (X76 = X78))) => 23.58/4.00 ((![X80:term,X82:term,X84:term]: 23.58/4.00 (lam(X80) != ap(X82,X84))) => 23.58/4.00 ((![X86:term,X88:term]: (~var(ap(X86,X88)))) => 23.58/4.00 ((![X90:term]: (~var(lam(X90)))) => 23.58/4.00 ((![X92:((term > $o))]: 23.58/4.00 ((![X94:term]: (var(X94) => X92(X94))) => 23.58/4.00 ((![X96:term,X98:term]: 23.58/4.00 (X92(X96) => (X92(X98) => X92(ap(X96,X98))))) => 23.58/4.00 ((![X100:term]: (X92(X100) => X92(lam(X100)))) => 23.58/4.00 (![X102:term]: X92(X102)))))) => 23.58/4.00 ((![X104:((term > $o)),X106:term,X108:subst]: 23.58/4.00 ((![X110:term]: 23.58/4.00 (var(X110) => X104(sub(X110,X108)))) => 23.58/4.00 (X104(X106) => 23.58/4.00 (![X112:term]: 23.58/4.00 (var(X112) => 23.58/4.00 X104(sub(X112,push(X106,X108)))))))) => 23.58/4.00 ((![X114:((term > $o))]: 23.58/4.00 ((![X116:term,X118:term]: 23.58/4.00 (X114(X116) => 23.58/4.00 (X114(X118) => X114(ap(X116,X118))))) => 23.58/4.00 ((![X120:term]: 23.58/4.00 ((![X122:term]: 23.58/4.00 (X114(X122) => 23.58/4.00 X114(sub(X120,push(X122,id))))) => 23.58/4.00 X114(lam(X120)))) => 23.58/4.00 (![X124:term,X126:subst]: 23.58/4.00 ((![X128:term]: 23.58/4.00 (var(X128) => X114(sub(X128,X126)))) => 23.58/4.00 X114(sub(X124,X126))))))) => 23.58/4.00 ((![X130:((term > $o))]: 23.58/4.00 ((![X132:term]: (var(X132) => X130(X132))) => 23.58/4.00 ((![X134:term,X136:term]: 23.58/4.00 (X130(X134) => 23.58/4.00 (X130(X136) => X130(ap(X134,X136))))) => 23.58/4.00 ((![X138:term]: 23.58/4.00 ((![X140:term]: 23.58/4.00 (X130(X140) => 23.58/4.00 X130(sub(X138,push(X140,id))))) => 23.58/4.00 X130(lam(X138)))) => 23.58/4.00 (![X142:term]: X130(X142)))))) => 23.58/4.00 (((![X144:subst]: (comp(X144,id) = X144)) & 23.58/4.00 (![X146:subst]: (comp(id,X146) = X146)) & 23.58/4.00 (![X148:subst,X150:subst,X152:subst]: 23.58/4.00 (comp(comp(X148,X150),X152) = 23.58/4.00 comp(X148,comp(X150,X152))))) => 23.58/4.00 (((![X154:term]: (sub(X154,id) = X154)) & 23.58/4.00 (![X156:term,X158:subst,X160:subst]: 23.58/4.00 (sub(sub(X156,X158),X160) = 23.58/4.00 sub(X156,comp(X158,X160))))) => 23.58/4.00 ((![X162:term,X164:term,X166:term,X168:term]: 23.58/4.00 ((ap(sub(X162,id),X166) = 23.58/4.00 ap(sub(X164,id),X168)) => 23.58/4.00 (X162 = X164))) => 23.58/4.00 ((![X170:term,X172:term,X174:term,X176:term]: 23.58/4.00 ((ap(sub(X170,id),X174) = 23.58/4.00 ap(sub(X172,id),X176)) => 23.58/4.00 (X174 = X176))) => 23.58/4.00 (![X178:((subst * term) > term)]: 23.58/4.00 ((![X180:subst,X182:term,X184:subst]: 23.58/4.00 (sub(X178(X180,X182),X184) = 23.58/4.00 X178(comp(X180,X184),sub(X182,X184)))) => 23.58/4.00 (![X186:((subst * term) > term)]: 23.58/4.00 ((![X188:subst,X190:term,X192:subst]: 23.58/4.00 (sub(X186(X188,X190),X192) = 23.58/4.00 X186(comp(X188,X192), 23.58/4.00 sub(X190,X192)))) => 23.58/4.00 ((lam(X178(sh,one)) = 23.58/4.00 lam(X186(sh,one))) => 23.58/4.00 (![X194:subst,X196:term]: 23.58/4.00 (X178(X194,X196) = 23.58/4.00 X186(X194,X196))))))))))))))))))))))))))))))))))))))). 23.58/4.00 tff(zf_stmt_1, negated_conjecture, 23.58/4.00 (~ 23.58/4.00 ((![X4:term,X6:term,X8:subst]: 23.58/4.00 (sub(ap(X4,X6),X8) = ap(sub(X4,X8),sub(X6,X8)))) => 23.58/4.00 ((![X10:term,X12:subst]: (sub(one,push(X10,X12)) = X10)) => 23.58/4.00 ((![X14:term]: (sub(X14,id) = X14)) => 23.58/4.00 ((![X16:term,X18:subst]: 23.58/4.00 (sub(lam(X16),X18) = lam(sub(X16,push(one,comp(X18,sh)))))) => 23.58/4.00 ((![X20:term,X22:subst,X24:subst]: 23.58/4.00 (sub(sub(X20,X22),X24) = sub(X20,comp(X22,X24)))) => 23.58/4.00 ((![X26:subst]: (comp(id,X26) = X26)) => 23.58/4.00 ((![X28:term,X30:subst]: (comp(sh,push(X28,X30)) = X30)) => 23.58/4.00 ((![X32:subst,X34:subst,X36:subst]: 23.58/4.00 (comp(comp(X32,X34),X36) = comp(X32,comp(X34,X36)))) => 23.58/4.00 ((![X38:term,X40:subst,X42:subst]: 23.58/4.00 (comp(push(X38,X40),X42) = push(sub(X38,X42),comp(X40,X42)))) => 23.58/4.00 ((![X44:subst]: (comp(X44,id) = X44)) => 23.58/4.00 ((push(one,sh) = id) => 23.58/4.00 ((![X46:subst]: (push(sub(one,X46),comp(sh,X46)) = X46)) => 23.58/4.00 (var(one) => 23.58/4.00 ((![X48:term]: (var(X48) => var(sub(X48,sh)))) => 23.58/4.00 ((![X50:((term > $o))]: 23.58/4.00 (X50(one) => 23.58/4.00 ((![X52:term]: 23.58/4.00 (var(X52) => (X50(X52) => X50(sub(X52,sh))))) => 23.58/4.00 (![X54:term]: (var(X54) => X50(X54)))))) => 23.58/4.00 ((![X56:term,X58:term,X60:term,X62:term]: 23.58/4.00 ((ap(X56,X60) = ap(X58,X62)) => (X56 = X58))) => 23.58/4.00 ((![X64:term,X66:term,X68:term,X70:term]: 23.58/4.00 ((ap(X64,X68) = ap(X66,X70)) => (X68 = X70))) => 23.58/4.00 ((![X72:term,X74:term]: 23.58/4.00 ((lam(X72) = lam(X74)) => (X72 = X74))) => 23.58/4.00 ((![X76:term,X78:term]: 23.58/4.00 ((sub(X76,sh) = sub(X78,sh)) => (X76 = X78))) => 23.58/4.00 ((![X80:term,X82:term,X84:term]: 23.58/4.00 (lam(X80) != ap(X82,X84))) => 23.58/4.00 ((![X86:term,X88:term]: (~var(ap(X86,X88)))) => 23.58/4.00 ((![X90:term]: (~var(lam(X90)))) => 23.58/4.00 ((![X92:((term > $o))]: 23.58/4.00 ((![X94:term]: (var(X94) => X92(X94))) => 23.58/4.00 ((![X96:term,X98:term]: 23.58/4.00 (X92(X96) => 23.58/4.00 (X92(X98) => X92(ap(X96,X98))))) => 23.58/4.00 ((![X100:term]: (X92(X100) => X92(lam(X100)))) => 23.58/4.00 (![X102:term]: X92(X102)))))) => 23.58/4.00 ((![X104:((term > $o)),X106:term,X108:subst]: 23.58/4.00 ((![X110:term]: 23.58/4.00 (var(X110) => X104(sub(X110,X108)))) => 23.58/4.00 (X104(X106) => 23.58/4.00 (![X112:term]: 23.58/4.00 (var(X112) => 23.58/4.00 X104(sub(X112,push(X106,X108)))))))) => 23.58/4.00 ((![X114:((term > $o))]: 23.58/4.00 ((![X116:term,X118:term]: 23.58/4.00 (X114(X116) => 23.58/4.00 (X114(X118) => X114(ap(X116,X118))))) => 23.58/4.00 ((![X120:term]: 23.58/4.00 ((![X122:term]: 23.58/4.00 (X114(X122) => 23.58/4.00 X114(sub(X120,push(X122,id))))) => 23.58/4.00 X114(lam(X120)))) => 23.58/4.00 (![X124:term,X126:subst]: 23.58/4.00 ((![X128:term]: 23.58/4.00 (var(X128) => X114(sub(X128,X126)))) => 23.58/4.00 X114(sub(X124,X126))))))) => 23.58/4.00 ((![X130:((term > $o))]: 23.58/4.00 ((![X132:term]: (var(X132) => X130(X132))) => 23.58/4.00 ((![X134:term,X136:term]: 23.58/4.00 (X130(X134) => 23.58/4.00 (X130(X136) => X130(ap(X134,X136))))) => 23.58/4.00 ((![X138:term]: 23.58/4.00 ((![X140:term]: 23.58/4.00 (X130(X140) => 23.58/4.00 X130(sub(X138,push(X140,id))))) => 23.58/4.00 X130(lam(X138)))) => 23.58/4.00 (![X142:term]: X130(X142)))))) => 23.58/4.00 (((![X144:subst]: (comp(X144,id) = X144)) & 23.58/4.00 (![X146:subst]: (comp(id,X146) = X146)) & 23.58/4.00 (![X148:subst,X150:subst,X152:subst]: 23.58/4.00 (comp(comp(X148,X150),X152) = 23.58/4.00 comp(X148,comp(X150,X152))))) => 23.58/4.00 (((![X154:term]: (sub(X154,id) = X154)) & 23.58/4.00 (![X156:term,X158:subst,X160:subst]: 23.58/4.00 (sub(sub(X156,X158),X160) = 23.58/4.00 sub(X156,comp(X158,X160))))) => 23.58/4.00 ((![X162:term,X164:term,X166:term,X168:term]: 23.58/4.00 ((ap(sub(X162,id),X166) = 23.58/4.00 ap(sub(X164,id),X168)) => 23.58/4.00 (X162 = X164))) => 23.58/4.00 ((![X170:term,X172:term,X174:term,X176:term]: 23.58/4.00 ((ap(sub(X170,id),X174) = 23.58/4.00 ap(sub(X172,id),X176)) => 23.58/4.00 (X174 = X176))) => 23.58/4.00 (![X178:((subst * term) > term)]: 23.58/4.00 ((![X180:subst,X182:term,X184:subst]: 23.58/4.00 (sub(X178(X180,X182),X184) = 23.58/4.00 X178(comp(X180,X184),sub(X182,X184)))) => 23.58/4.00 (![X186:((subst * term) > term)]: 23.58/4.00 ((![X188:subst,X190:term,X192:subst]: 23.58/4.00 (sub(X186(X188,X190),X192) = 23.58/4.00 X186(comp(X188,X192), 23.58/4.00 sub(X190,X192)))) => 23.58/4.00 ((lam(X178(sh,one)) = 23.58/4.00 lam(X186(sh,one))) => 23.58/4.00 (![X194:subst,X196:term]: 23.58/4.00 (X178(X194,X196) = 23.58/4.00 X186(X194,X196)))))))))))))))))))))))))))))))))))))))). 23.58/4.00 tff('37', plain, sk_X178(sk_X194, sk_X196) != sk_X186(sk_X194, sk_X196), 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('38', plain, 23.58/4.00 ![X313 : subst, X314 : term]: comp(sh, push(X314, X313)) = X313, 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('39', plain, 23.58/4.00 ![X343 : subst, X344 : subst, X345 : term]: 23.58/4.00 sub(sk_X186(X343, X345), X344) 23.58/4.00 = sk_X186(comp(X343, X344), sub(X345, X344)), 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('40', plain, lam(sk_X178(sh, one)) = lam(sk_X186(sh, one)), 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('41', plain, 23.58/4.00 ![X383 : term, X384 : subst]: sub(one, push(X383, X384)) = X383, 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('42', plain, 23.58/4.00 ![X346 : subst, X347 : subst, X348 : term]: 23.58/4.00 sub(sk_X178(X346, X348), X347) 23.58/4.00 = sk_X178(comp(X346, X347), sub(X348, X347)), 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('43', plain, 23.58/4.00 ![X368 : term, X369 : term]: (X369 = X368 | lam(X369) != lam(X368)), 23.58/4.00 inference('cnf', [status(esa)], [zf_stmt_1])). 23.58/4.00 tff('44', plain, $false, 23.58/4.00 inference('eprover', [status(thm)], 23.58/4.00 ['37', '38', '39', '40', '41', '42', '43'])). 23.58/4.00 23.58/4.00 % SZS output end Refutation 23.58/4.00 23.58/4.00 23.58/4.00 % Terminating... 23.58/4.03 % Runner terminated. 23.58/4.05 % Zipperpin 1.5 exiting 23.58/4.05 EOF