%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP128^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:52 AM UTC 2026
% Result : Theorem 63.69s 44.20s
% Output : Refutation 64.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 95
% Syntax : Number of formulae : 192 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 556 ( 210 equ; 18 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2829 ( 6 ~; 0 |; 4 &;2609 @)
% ( 0 <=>; 210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 568 ( 568 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 5 con; 0-8 aty)
% Number of variables : 1038 ( 44 ^; 988 !; 6 ?;1038 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_type,type,
d: $tType ).
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(plus_decl,type,
plus:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(bNF_rel_fun_decl,type,
bNF_rel_fun:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > $o ) > ( TB > TA > $o ) > ( TD > TB ) > ( TC > TA ) > $o ) ).
thf(ffold_decl,type,
ffold:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > TA > ( fset @ TB ) > TA ) ).
thf(finite100568337ommute_decl,type,
finite100568337ommute:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(finite_comp_fun_idem_decl,type,
finite_comp_fun_idem:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(finite852775215axioms_decl,type,
finite852775215axioms:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(finite_fold_graph_decl,type,
finite_fold_graph:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > TA > ( set @ TB ) > TA > $o ) ).
thf(finite_folding_idem_decl,type,
finite_folding_idem:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(finite1921348288axioms_decl,type,
finite1921348288axioms:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(comp_decl,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(fold_mset_decl,type,
fold_mset:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > TA > ( multiset @ TB ) > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_decl,type,
a2: a > b > $o ).
thf(b2_decl,type,
b2: c > d > $o ).
thf(f1_decl,type,
f1: a > c > c ).
thf(f2_decl,type,
f2: b > d > d ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_rewriteR__comp__comp2) ).
thf(138,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( TA > TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_fun_Orel__eq) ).
thf(173,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( TA > TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > $o,B: TC > TB > $o,C: TA > TC,D: TA > TB,E: TA] :
( ( bNF_rel_fun @ TA @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( B @ ( C @ E ) @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rel__funD2) ).
thf(327,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > $o,B: TC > TB > $o,C: TA > TC,D: TA > TB,E: TA] :
( ( bNF_rel_fun @ TA @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( B @ ( C @ E ) @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_rewriteR__comp__comp) ).
thf(338,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(24,axiom,
! [TA: $tType] : ( ab_semigroup_add @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Oab__semigroup__add_10) ).
thf(154,plain,
! [TA: $tType] : ( ab_semigroup_add @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(67,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_add__right__imp__eq) ).
thf(308,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(12,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_union__left__cancel) ).
thf(120,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ! [B: TA,C: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ C ) )
= ( comp @ TB @ TB @ TB @ ( A @ C ) @ ( A @ B ) ) )
=> ( finite100568337ommute @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_comp__fun__commute_Ointro) ).
thf(385,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ! [B: TA,C: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ C ) )
= ( comp @ TB @ TB @ TB @ ( A @ C ) @ ( A @ B ) ) )
=> ( finite100568337ommute @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rel__funE) ).
thf(142,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType] :
( ( finite100568337ommute @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
! [B: TA,C: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ C ) )
= ( comp @ TB @ TB @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_comp__fun__commute__def) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( finite100568337ommute @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
! [B: TA,C: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ C ) )
= ( comp @ TB @ TB @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(88,axiom,
finite100568337ommute @ b @ d @ f2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(372,plain,
finite100568337ommute @ b @ d @ f2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite_folding_idem @ TA @ TB @ A )
=> ( finite1921348288axioms @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_folding__idem_Oaxioms_I2_J) ).
thf(110,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite_folding_idem @ TA @ TB @ A )
=> ( finite1921348288axioms @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA,C: TB,D: fset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( A @ B @ ( ffold @ TA @ TB @ A @ C @ D ) )
= ( ffold @ TA @ TB @ A @ ( A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_comp__fun__commute_Offold__fun__left__comm) ).
thf(357,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA,C: TB,D: fset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( A @ B @ ( ffold @ TA @ TB @ A @ C @ D ) )
= ( ffold @ TA @ TB @ A @ ( A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(72,axiom,
! [TA: $tType] : ( plus @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Oplus_14) ).
thf(325,plain,
! [TA: $tType] : ( plus @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TA > $o,B: TD > TB > $o] : ( bNF_rel_fun @ ( TE > TD ) @ ( TA > TB ) @ ( ( TC > TE ) > TC > TD ) @ ( ( TC > TA ) > TC > TB ) @ ( bNF_rel_fun @ TE @ TA @ TD @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TC > TE ) @ ( TC > TA ) @ ( TC > TD ) @ ( TC > TB ) @ ( bNF_rel_fun @ TC @ TC @ TE @ TA @ ( (=) @ TC ) @ A ) @ ( bNF_rel_fun @ TC @ TC @ TD @ TB @ ( (=) @ TC ) @ B ) ) @ ( comp @ TE @ TD @ TC ) @ ( comp @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fun_Omap__transfer) ).
thf(152,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TA > $o,B: TD > TB > $o] : ( bNF_rel_fun @ ( TE > TD ) @ ( TA > TB ) @ ( ( TC > TE ) > TC > TD ) @ ( ( TC > TA ) > TC > TB ) @ ( bNF_rel_fun @ TE @ TA @ TD @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TC > TE ) @ ( TC > TA ) @ ( TC > TD ) @ ( TC > TB ) @ ( bNF_rel_fun @ TC @ TC @ TE @ TA @ ( (=) @ TC ) @ A ) @ ( bNF_rel_fun @ TC @ TC @ TD @ TB @ ( (=) @ TC ) @ B ) ) @ ( comp @ TE @ TD @ TC ) @ ( comp @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > $o] : ( bNF_rel_fun @ ( TA > TB ) @ ( TA > TB ) @ ( ( TD > TA ) > TD > TB ) @ ( ( TC > TA ) > TC > TB ) @ ( (=) @ ( TA > TB ) ) @ ( bNF_rel_fun @ ( TD > TA ) @ ( TC > TA ) @ ( TD > TB ) @ ( TC > TB ) @ ( bNF_rel_fun @ TD @ TC @ TA @ TA @ A @ ( (=) @ TA ) ) @ ( bNF_rel_fun @ TD @ TC @ TB @ TB @ A @ ( (=) @ TB ) ) ) @ ( comp @ TA @ TB @ TD ) @ ( comp @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_o__rsp_I2_J) ).
thf(289,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > $o] : ( bNF_rel_fun @ ( TA > TB ) @ ( TA > TB ) @ ( ( TD > TA ) > TD > TB ) @ ( ( TC > TA ) > TC > TB ) @ ( (=) @ ( TA > TB ) ) @ ( bNF_rel_fun @ ( TD > TA ) @ ( TC > TA ) @ ( TD > TB ) @ ( TC > TB ) @ ( bNF_rel_fun @ TD @ TC @ TA @ TA @ A @ ( (=) @ TA ) ) @ ( bNF_rel_fun @ TD @ TC @ TB @ TB @ A @ ( (=) @ TB ) ) ) @ ( comp @ TA @ TB @ TD ) @ ( comp @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(54,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_union__lcomm) ).
thf(261,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TC,B: TA > TB] :
( ( finite100568337ommute @ TB @ TC @ A )
=> ( finite100568337ommute @ TA @ TC @ ( comp @ TB @ ( TC > TC ) @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_comp__fun__commute_Ocomp__comp__fun__commute) ).
thf(376,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TC,B: TA > TB] :
( ( finite100568337ommute @ TB @ TC @ A )
=> ( finite100568337ommute @ TA @ TC @ ( comp @ TB @ ( TC > TC ) @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(51,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add__left__cancel) ).
thf(253,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(7,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_2) ).
thf(106,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( finite1921348288axioms @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_folding__idem__axioms__def) ).
thf(238,plain,
! [TA: $tType,TB: $tType] :
( ( finite1921348288axioms @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA,C: TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ C ) )
= ( comp @ TB @ TB @ TB @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_comp__fun__commute_Ocomp__fun__commute) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA,C: TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ C ) )
= ( comp @ TB @ TB @ TB @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) )
=> ( finite852775215axioms @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_comp__fun__idem__axioms_Ointro) ).
thf(293,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) )
=> ( finite852775215axioms @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(41,axiom,
! [TA: $tType] :
( ( plus_plus @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] : ( plus_plus @ ( multiset @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_union__commute) ).
thf(206,plain,
! [TA: $tType] :
( ( plus_plus @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] : ( plus_plus @ ( multiset @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Let__transfer) ).
thf(248,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TB,B: TC,C: TC,D: TA > TB] :
( ( finite100568337ommute @ TC @ TB @ A )
=> ( ( comp @ TB @ TB @ TA @ ( A @ B ) @ ( comp @ TB @ TB @ TA @ ( A @ C ) @ D ) )
= ( comp @ TB @ TB @ TA @ ( A @ C ) @ ( comp @ TB @ TB @ TA @ ( A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_comp__fun__commute_Ocommute__left__comp) ).
thf(380,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TB,B: TC,C: TC,D: TA > TB] :
( ( finite100568337ommute @ TC @ TB @ A )
=> ( ( comp @ TB @ TB @ TA @ ( A @ B ) @ ( comp @ TB @ TB @ TA @ ( A @ C ) @ D ) )
= ( comp @ TB @ TB @ TA @ ( A @ C ) @ ( comp @ TB @ TB @ TA @ ( A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_apply__rsp_H) ).
thf(270,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: TB,D: TA] :
( ( finite100568337ommute @ TB @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_comp__fun__commute_Ofun__left__comm) ).
thf(366,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: TB,D: TA] :
( ( finite100568337ommute @ TB @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(5,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ( plus @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oplus) ).
thf(102,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ( plus @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( finite852775215axioms @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_comp__fun__idem__axioms__def) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( finite852775215axioms @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA] :
( ( finite_comp_fun_idem @ TA @ TB @ A )
=> ( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_comp__fun__idem_Ocomp__fun__idem) ).
thf(165,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA] :
( ( finite_comp_fun_idem @ TA @ TB @ A )
=> ( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(39,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add_Oleft__cancel) ).
thf(197,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1,conjecture,
finite100568337ommute @ a @ c @ f1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite100568337ommute @ a @ c @ f1 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(97,plain,
~ ( finite100568337ommute @ a @ c @ f1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_add__left__imp__eq) ).
thf(156,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add_Oleft__commute) ).
thf(188,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(95,axiom,
bNF_rel_fun @ a @ b @ ( c > c ) @ ( d > d ) @ a2 @ ( bNF_rel_fun @ c @ d @ c @ d @ b2 @ b2 ) @ f1 @ f2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C12_C) ).
thf(388,plain,
bNF_rel_fun @ a @ b @ ( c > c ) @ ( d > d ) @ a2 @ ( bNF_rel_fun @ c @ d @ c @ d @ b2 @ b2 ) @ f1 @ f2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(52,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_add_Oright__cancel) ).
thf(256,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_rewriteL__comp__comp) ).
thf(193,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > TB,D: TA > TB > TB,E: TB] :
( ! [F: TA,G: TB] :
( ( member @ TA @ F @ A )
=> ( ( member @ TB @ G @ B )
=> ( ( C @ F @ G )
= ( D @ F @ G ) ) ) )
=> ( ! [F: TA,G: TB] :
( ( member @ TA @ F @ A )
=> ( ( member @ TB @ G @ B )
=> ( member @ TB @ ( D @ F @ G ) @ B ) ) )
=> ( ( member @ TB @ E @ B )
=> ( ( finite_fold_graph @ TA @ TB @ C @ E @ A )
= ( finite_fold_graph @ TA @ TB @ D @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_fold__graph__closed__eq) ).
thf(212,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > TB,D: TA > TB > TB,E: TB] :
( ! [F: TA,G: TB] :
( ( member @ TA @ F @ A )
=> ( ( member @ TB @ G @ B )
=> ( ( C @ F @ G )
= ( D @ F @ G ) ) ) )
=> ( ! [F: TA,G: TB] :
( ( member @ TA @ F @ A )
=> ( ( member @ TB @ G @ B )
=> ( member @ TB @ ( D @ F @ G ) @ B ) ) )
=> ( ( member @ TB @ E @ B )
=> ( ( finite_fold_graph @ TA @ TB @ C @ E @ A )
= ( finite_fold_graph @ TA @ TB @ D @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [TA: $tType] : ( comm_monoid_add @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Ocomm__monoid__add_11) ).
thf(128,plain,
! [TA: $tType] : ( comm_monoid_add @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB] :
( ! [E: TD,F: TA] :
( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__funI) ).
thf(244,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB] :
( ! [E: TD,F: TA] :
( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TB,C: multiset @ TA,D: multiset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( fold_mset @ TA @ TB @ A @ B @ ( plus_plus @ ( multiset @ TA ) @ C @ D ) )
= ( fold_mset @ TA @ TB @ A @ ( fold_mset @ TA @ TB @ A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_comp__fun__commute_Ofold__mset__union) ).
thf(360,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TB,C: multiset @ TA,D: multiset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( fold_mset @ TA @ TB @ A @ B @ ( plus_plus @ ( multiset @ TA ) @ C @ D ) )
= ( fold_mset @ TA @ TB @ A @ ( fold_mset @ TA @ TB @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(68,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_group__cancel_Oadd1) ).
thf(311,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(55,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_union__right__cancel) ).
thf(264,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA > TF > $o,B: TD > TC > $o,C: TE > TB > $o,D: TA > TD > TE,E: TF > TC > TB] :
( ( bNF_rel_fun @ TA @ TF @ ( TD > TE ) @ ( TC > TB ) @ A @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C ) @ D @ E )
= ( ! [F: TA,G: TF] :
( ( A @ F @ G )
=> ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C @ ( D @ F ) @ ( E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__fun__def__butlast) ).
thf(149,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA > TF > $o,B: TD > TC > $o,C: TE > TB > $o,D: TA > TD > TE,E: TF > TC > TB] :
( ( bNF_rel_fun @ TA @ TF @ ( TD > TE ) @ ( TC > TB ) @ A @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C ) @ D @ E )
= ( ! [F: TA,G: TF] :
( ( A @ F @ G )
=> ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C @ ( D @ F ) @ ( E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add_Ocommute) ).
thf(180,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( E @ G @ H )
=> ( A @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( B @ G @ H )
=> ( F @ G @ H ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rel__fun__mono) ).
thf(296,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( E @ G @ H )
=> ( A @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( B @ G @ H )
=> ( F @ G @ H ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comp__eq__dest__lhs) ).
thf(176,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_let__rsp) ).
thf(191,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(62,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Orderings_Opreorder) ).
thf(291,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > TA > $o,B: TE > TB > $o,C: TD > TC > $o] : ( bNF_rel_fun @ ( TF > TE ) @ ( TA > TB ) @ ( ( TD > TF ) > TD > TE ) @ ( ( TC > TA ) > TC > TB ) @ ( bNF_rel_fun @ TF @ TA @ TE @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > TF ) @ ( TC > TA ) @ ( TD > TE ) @ ( TC > TB ) @ ( bNF_rel_fun @ TD @ TC @ TF @ TA @ C @ A ) @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ C @ B ) ) @ ( comp @ TF @ TE @ TD ) @ ( comp @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_o__rsp_I1_J) ).
thf(259,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > TA > $o,B: TE > TB > $o,C: TD > TC > $o] : ( bNF_rel_fun @ ( TF > TE ) @ ( TA > TB ) @ ( ( TD > TF ) > TD > TE ) @ ( ( TC > TA ) > TC > TB ) @ ( bNF_rel_fun @ TF @ TA @ TE @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > TF ) @ ( TC > TA ) @ ( TD > TE ) @ ( TC > TB ) @ ( bNF_rel_fun @ TD @ TC @ TF @ TA @ C @ A ) @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ C @ B ) ) @ ( comp @ TF @ TE @ TD ) @ ( comp @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(20,axiom,
! [TA: $tType] : ( cancel_semigroup_add @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Ocancel__semigroup__add) ).
thf(144,plain,
! [TA: $tType] : ( cancel_semigroup_add @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TC] :
( ( ! [C: TA] :
? [D: TB] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: TA > TB] :
( B
= ( comp @ TB @ TC @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_function__factors__right) ).
thf(335,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TC] :
( ( ! [C: TA] :
? [D: TB] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: TA > TB] :
( B
= ( comp @ TB @ TC @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TC,B: TA > TB] :
( ( finite_comp_fun_idem @ TB @ TC @ A )
=> ( finite_comp_fun_idem @ TA @ TC @ ( comp @ TB @ ( TC > TC ) @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_comp__fun__idem_Ocomp__comp__fun__idem) ).
thf(236,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TC,B: TA > TB] :
( ( finite_comp_fun_idem @ TB @ TC @ A )
=> ( finite_comp_fun_idem @ TA @ TC @ ( comp @ TB @ ( TC > TC ) @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TD @ TB @ TA @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comp__apply__eq) ).
thf(159,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TD @ TB @ TA @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comp__eq__dest) ).
thf(274,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_rewriteL__comp__comp2) ).
thf(318,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(3,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ( semigroup_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Osemigroup__add) ).
thf(98,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ( semigroup_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(78,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add__right__cancel) ).
thf(345,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(8,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ D )
=> ( member @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_set__plus__intro) ).
thf(108,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ D )
=> ( member @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TB] :
( ! [C: TB] : ( A @ C @ C )
=> ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_fun_Orel__refl) ).
thf(130,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TB] :
( ! [C: TB] : ( A @ C @ C )
=> ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_comp__def) ).
thf(135,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_fun_Omap__comp) ).
thf(267,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(47,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add_Oassoc) ).
thf(241,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(162,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA] :
( ( finite_folding_idem @ TA @ TB @ A )
=> ( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_folding__idem_Ocomp__fun__idem) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA] :
( ( finite_folding_idem @ TA @ TB @ A )
=> ( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder_3) ).
thf(112,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( finite852775215axioms @ TA @ TB @ A )
=> ( finite_comp_fun_idem @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comp__fun__idem_Ointro) ).
thf(355,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( finite852775215axioms @ TA @ TB @ A )
=> ( finite_comp_fun_idem @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comp__apply) ).
thf(342,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(13,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_multi__union__self__other__eq) ).
thf(123,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: TC > TB] :
( ( ! [C: TC,D: TC] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: TA > TB] :
( B
= ( comp @ TA @ TB @ TC @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_function__factors__left) ).
thf(250,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: TC > TB] :
( ( ! [C: TC,D: TC] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: TA > TB] :
( B
= ( comp @ TA @ TB @ TC @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA,C: set @ TB,D: TA,E: TA] :
( ( finite100568337ommute @ TB @ TA @ A )
=> ( ( finite_fold_graph @ TB @ TA @ A @ B @ C @ D )
=> ( ( finite_fold_graph @ TB @ TA @ A @ B @ C @ E )
=> ( E = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_comp__fun__commute_Ofold__graph__determ) ).
thf(363,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA,C: set @ TB,D: TA,E: TA] :
( ( finite100568337ommute @ TB @ TA @ A )
=> ( ( finite_fold_graph @ TB @ TA @ A @ B @ C @ D )
=> ( ( finite_fold_graph @ TB @ TA @ A @ B @ C @ E )
=> ( E = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(6,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ocomm__monoid__add) ).
thf(104,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA,C: TB,D: multiset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( A @ B @ ( fold_mset @ TA @ TB @ A @ C @ D ) )
= ( fold_mset @ TA @ TB @ A @ ( A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_comp__fun__commute_Ofold__mset__fun__left__comm) ).
thf(351,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB,B: TA,C: TB,D: multiset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( A @ B @ ( fold_mset @ TA @ TB @ A @ C @ D ) )
= ( fold_mset @ TA @ TB @ A @ ( A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rel__funD) ).
thf(186,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( plus_plus @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( A
= ( plus_plus @ TA @ D @ E ) )
=> ( ( member @ TA @ D @ B )
=> ~ ( member @ TA @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_set__plus__elim) ).
thf(114,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( plus_plus @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( A
= ( plus_plus @ TA @ D @ E ) )
=> ( ( member @ TA @ D @ B )
=> ~ ( member @ TA @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
! [TA: $tType] : ( semigroup_add @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Osemigroup__add_12) ).
thf(171,plain,
! [TA: $tType] : ( semigroup_add @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(91,axiom,
! [TA: $tType] : ( finite100568337ommute @ ( multiset @ TA ) @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_comp__fun__commute__plus__mset) ).
thf(378,plain,
! [TA: $tType] : ( finite100568337ommute @ ( multiset @ TA ) @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > TA > $o,B: TE > TB > $o,C: TD > TC > $o] : ( bNF_rel_fun @ ( TF > TE ) @ ( TA > TB ) @ ( ( TD > TF ) > TD > TE ) @ ( ( TC > TA ) > TC > TB ) @ ( bNF_rel_fun @ TF @ TA @ TE @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > TF ) @ ( TC > TA ) @ ( TD > TE ) @ ( TC > TB ) @ ( bNF_rel_fun @ TD @ TC @ TF @ TA @ C @ A ) @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ C @ B ) ) @ ( comp @ TF @ TE @ TD ) @ ( comp @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comp__transfer) ).
thf(272,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > TA > $o,B: TE > TB > $o,C: TD > TC > $o] : ( bNF_rel_fun @ ( TF > TE ) @ ( TA > TB ) @ ( ( TD > TF ) > TD > TE ) @ ( ( TC > TA ) > TC > TB ) @ ( bNF_rel_fun @ TF @ TA @ TE @ TB @ A @ B ) @ ( bNF_rel_fun @ ( TD > TF ) @ ( TC > TA ) @ ( TD > TE ) @ ( TC > TB ) @ ( bNF_rel_fun @ TD @ TC @ TF @ TA @ C @ A ) @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ C @ B ) ) @ ( comp @ TF @ TE @ TD ) @ ( comp @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite_comp_fun_idem @ TA @ TB @ A )
=> ( finite100568337ommute @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_comp__fun__idem_Oaxioms_I1_J) ).
thf(383,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite_comp_fun_idem @ TA @ TB @ A )
=> ( finite100568337ommute @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comp__cong) ).
thf(315,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comp__assoc) ).
thf(168,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comp__eq__elim) ).
thf(146,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) )
=> ( finite1921348288axioms @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_folding__idem__axioms_Ointro) ).
thf(183,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ! [B: TA] :
( ( comp @ TB @ TB @ TB @ ( A @ B ) @ ( A @ B ) )
= ( A @ B ) )
=> ( finite1921348288axioms @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( finite_comp_fun_idem @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
( ( finite100568337ommute @ TA @ TB @ A )
& ( finite852775215axioms @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_comp__fun__idem__def) ).
thf(373,plain,
! [TA: $tType,TB: $tType] :
( ( finite_comp_fun_idem @ TA @ TB )
= ( ^ [A: TA > TB > TB] :
( ( finite100568337ommute @ TA @ TB @ A )
& ( finite852775215axioms @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
= ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_type__copy__map__cong0) ).
thf(305,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
= ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite_comp_fun_idem @ TA @ TB @ A )
=> ( finite852775215axioms @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_comp__fun__idem_Oaxioms_I2_J) ).
thf(126,plain,
! [TA: $tType,TB: $tType,A: TA > TB > TB] :
( ( finite_comp_fun_idem @ TA @ TB @ A )
=> ( finite852775215axioms @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(74,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ C )
= ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_union__assoc) ).
thf(332,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ C )
= ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD > TA > $o,C: TC > TB > $o,D: TC > TB > $o,E: TD > TC,F: TA > TB] :
( ! [G: TD,H: TA] :
( ( A @ G @ H )
=> ( B @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( C @ G @ H )
=> ( D @ G @ H ) )
=> ( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ B @ C @ E @ F )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_rel__fun__mono_H) ).
thf(200,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD > TA > $o,C: TC > TB > $o,D: TC > TB > $o,E: TD > TC,F: TA > TB] :
( ! [G: TD,H: TA] :
( ( A @ G @ H )
=> ( B @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( C @ G @ H )
=> ( D @ G @ H ) )
=> ( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ B @ C @ E @ F )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA,C: set @ TB,D: TA,E: set @ TA,F: TB > TA > TA] :
( ( finite_fold_graph @ TB @ TA @ A @ B @ C @ D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ C )
=> ( ( member @ TA @ H @ E )
=> ( ( F @ G @ H )
= ( A @ G @ H ) ) ) )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ C )
=> ( ( member @ TA @ H @ E )
=> ( member @ TA @ ( A @ G @ H ) @ E ) ) )
=> ( ( member @ TA @ B @ E )
=> ( ( finite_fold_graph @ TB @ TA @ F @ B @ C @ D )
& ( member @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_fold__graph__closed__lemma) ).
thf(277,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA,C: set @ TB,D: TA,E: set @ TA,F: TB > TA > TA] :
( ( finite_fold_graph @ TB @ TA @ A @ B @ C @ D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ C )
=> ( ( member @ TA @ H @ E )
=> ( ( F @ G @ H )
= ( A @ G @ H ) ) ) )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ C )
=> ( ( member @ TA @ H @ E )
=> ( member @ TA @ ( A @ G @ H ) @ E ) ) )
=> ( ( member @ TA @ B @ E )
=> ( ( finite_fold_graph @ TB @ TA @ F @ B @ C @ D )
& ( member @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TB,B: TA > TC > TC,C: TC > TB,D: TC,E: multiset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( finite100568337ommute @ TA @ TC @ B )
=> ( ! [F: TA,G: TC] :
( ( C @ ( B @ F @ G ) )
= ( A @ F @ ( C @ G ) ) )
=> ( ( C @ ( fold_mset @ TA @ TC @ B @ D @ E ) )
= ( fold_mset @ TA @ TB @ A @ ( C @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_comp__fun__commute_Ofold__mset__fusion) ).
thf(369,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TB,B: TA > TC > TC,C: TC > TB,D: TC,E: multiset @ TA] :
( ( finite100568337ommute @ TA @ TB @ A )
=> ( ( finite100568337ommute @ TA @ TC @ B )
=> ( ! [F: TA,G: TC] :
( ( C @ ( B @ F @ G ) )
= ( A @ F @ ( C @ G ) ) )
=> ( ( C @ ( fold_mset @ TA @ TC @ B @ D @ E ) )
= ( fold_mset @ TA @ TB @ A @ ( C @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: TA] :
( ( finite_comp_fun_idem @ TB @ TA @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comp__fun__idem_Ofun__left__idem) ).
thf(322,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: TA] :
( ( finite_comp_fun_idem @ TB @ TA @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(81,axiom,
finite100568337ommute @ a @ c @ f1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(354,plain,
finite100568337ommute @ a @ c @ f1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(44,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_group__cancel_Oadd2) ).
thf(232,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(4,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ab_semigroup_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oab__semigroup__add) ).
thf(100,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ab_semigroup_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(392,plain,
$false,
inference(e,[status(thm)],[138,173,327,338,154,308,120,385,142,389,372,110,357,325,152,289,261,376,253,106,238,348,293,206,248,380,270,366,102,302,165,197,97,156,188,388,256,193,212,128,244,360,311,264,149,180,296,176,191,291,259,144,335,236,159,274,318,98,345,108,130,135,267,241,162,209,112,355,342,123,250,363,104,351,186,114,171,378,272,383,315,168,146,183,373,305,126,332,200,277,369,322,354,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP128^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n001.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 20:03:36 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.33/1.26 % [INFO] Parsing done (454ms).
% 2.33/1.28 % [INFO] Running in sequential loop mode.
% 3.88/1.68 % [INFO] eprover registered as external prover.
% 3.88/1.69 % [INFO] Scanning for conjecture ...
% 4.37/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 283 axioms. Running axiom selection ...
% 4.59/1.96 % [INFO] Axiom selection finished. Selected 94 axioms (removed 189 axioms).
% 5.54/2.20 % [INFO] Problem is higher-order (TPTP THF).
% 5.54/2.23 % [INFO] Type checking passed.
% 5.54/2.23 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 63.44/44.19 % External prover 'e' found a proof!
% 63.44/44.19 % [INFO] Killing All external provers ...
% 63.69/44.20 % Time passed: 43843ms (effective reasoning time: 42912ms)
% 63.69/44.20 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 63.69/44.20 % Axioms used in derivation (94): fact_44_comp__apply__eq, fact_24_o__rsp_I1_J, fact_62_rel__funE, fact_125_add__left__imp__eq, fact_55_type__copy__map__cong0, tcon_Multiset_Omultiset___Orderings_Opreorder, tcon_Multiset_Omultiset___Groups_Ocomm__monoid__add_11, fact_94_union__commute, fact_23_o__rsp_I2_J, fact_49_comp__eq__dest__lhs, fact_92_union__assoc, fact_120_add_Oassoc, fact_20_rel__funI, fact_10_comp__fun__commute__def, fact_0_assms_I2_J, fact_106_set__plus__intro, fact_37_let__rsp, fact_38_rel__funD, fact_27_comp__fun__idem_Ointro, fact_104_add__right__cancel, fact_117_group__cancel_Oadd1, fact_135_folding__idem_Ocomp__fun__idem, fact_98_comp__fun__commute__plus__mset, fact_123_add_Ocommute, fact_86_comp__fun__commute_Ofold__mset__union, tcon_Set_Oset___Groups_Osemigroup__add, fact_4_comp__fun__commute_Ofold__mset__fusion, fact_42_rewriteL__comp__comp, fact_56_function__factors__right, fact_36_rel__fun__mono, fact_105_add__left__cancel, fact_12_comp__fun__commute_Ocomp__fun__commute, fact_53_comp__def, fact_121_add_Oleft__cancel, fact_6_comp__fun__idem_Oaxioms_I1_J, fact_2_assms_I3_J, fact_14_fold__graph__closed__lemma, fact_33_fun_Orel__refl, fact_9_comp__fun__commute_Ocomp__comp__fun__commute, fact_118_group__cancel_Oadd2, fact_26_comp__transfer, fact_119_set__plus__elim, fact_130_folding__idem_Oaxioms_I2_J, fact_30_comp__fun__idem__axioms_Ointro, fact_51_comp__eq__dest, fact_16_comp__fun__idem_Ofun__left__idem, fact_61_apply__rsp_H, fact_11_comp__fun__commute_Ointro, fact_7_comp__fun__commute_Ofold__graph__determ, fact_60_rel__funD2, fact_54_Let__transfer, fact_17_comp__fun__idem_Ocomp__comp__fun__idem, fact_28_comp__fun__idem__def, fact_41_rewriteR__comp__comp, tcon_Set_Oset___Groups_Ocomm__monoid__add, fact_43_fun_Omap__comp, fact_95_union__left__cancel, tcon_Multiset_Omultiset___Groups_Oplus_14, fact_15_comp__fun__idem_Ocomp__fun__idem, fact_31_comp__fun__idem__axioms__def, fact_39_rewriteR__comp__comp2, fact_122_add_Oright__cancel, fact_57_function__factors__left, fact_50_comp__eq__elim, fact_34_fun_Orel__eq, tcon_Set_Oset___Groups_Oab__semigroup__add, fact_3__C12_C, fact_19_comp__apply, fact_93_union__lcomm, fact_25_fun_Omap__transfer, fact_97_multi__union__self__other__eq, fact_1_comp__fun__commute_Ofun__left__comm, fact_96_union__right__cancel, fact_22_rel__fun__def__butlast, tcon_Multiset_Omultiset___Groups_Oab__semigroup__add_10, fact_126_add__right__imp__eq, fact_13_fold__graph__closed__eq, fact_115_ab__semigroup__add__class_Oadd__ac_I1_J, tcon_Set_Oset___Orderings_Opreorder_2, fact_40_rewriteL__comp__comp2, tcon_Multiset_Omultiset___Groups_Ocancel__semigroup__add, fact_58_comp__cong, fact_18_comp__fun__commute_Ocommute__left__comp, tcon_fun___Orderings_Opreorder_3, fact_83_folding__idem__axioms_Ointro, fact_8_comp__fun__commute_Offold__fun__left__comm, tcon_Set_Oset___Groups_Oplus, fact_124_add_Oleft__commute, fact_29_comp__fun__idem_Oaxioms_I2_J, fact_52_comp__assoc, fact_35_rel__fun__mono_H, tcon_Multiset_Omultiset___Groups_Osemigroup__add_12, fact_5_comp__fun__commute_Ofold__mset__fun__left__comm, fact_82_folding__idem__axioms__def
% 63.69/44.20 % No. of inferences in proof: 192
% 63.69/44.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 43843 ms resp. 42912 ms w/o parsing
% 64.20/44.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.20/44.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------